reliable and good product
7 0 Reply
Mathematics
Calculus Early Transcendentals Textbook Questions And Answers
US$14.99 US$24.00
b Chapter: 3 -Problem: 50 /b Find the limit. Transcribed Image Text: sinx – 1 lim x?1 x? + x – 2 brbAnswer Preview/b: sin x 1 lim x 1 x … brbr,b Chapter:
Description
Chapter: 3 -Problem: 50 >> Find the limit. Transcribed Image Text: sin(x – 1) lim x?1 x? + x – 2Answer Preview: sin x 1 lim x 1 x …
, Chapter: 16 -Problem: 10 >> Evaluate the line integral, where C is the given curve.?C y2z ds, C is the line segment from (3, 1, 2) to (1, 2, 5)
Answer Preview: Parametric equations for C…
, Chapter: 10 -Problem: 14 >> Sketch the polar curve.r = 2 cos(?/2)
Answer Preview: r 2 cos 0 2 The curve …
, Chapter: 11 -Problem: 38 >> For what values of p does the series converge? Transcribed Image Text: E-2 1/(nº In n) n=2
Answer Preview: Clearly if p 0 then the series diverges since lim 1 n Inn 1 n In n and n 2 n ln …
, Chapter: 16 -Problem: 9 >> Suppose F is a vector field on R3. (a) Define curl F. (b) Define div F.(c) If F is a velocity field in fluid flow, what are the physical interpretations of curl F and div F?
Answer Preview: Suppose F is a vector field on R 3 then Curl F The curl of a vector f…
, Chapter: 14 -Problem: 39 >> If z = y + f (x2 - y2), where f is differentiable, show that y ?z/?x + x ?z/?y = x
Answer Preview: Az z x 2xf x y oz …
, Chapter: 15 -Problem: 8 >> Find the mass and center of mass of the lamina that occupies the region D and has the given density function p. D is bounded by y = x + 2 and y = x2; (x, y) = kx2
Answer Preview: The boundary curves intersect when x 2 x D x y 1 x 2 x y x 2 m S kx dy …
, Chapter: 4 -Problem: 76 >> What happens if you try to use 1’Hospital’s Rule to find the limit? Evaluate the limit using another method. Transcribed Image Text: sec x lim /2) ?— (?- tan x
Answer Preview: Repeated applications of 1Hospitals Rule re…
, Chapter: 7 -Problem: 32 >> Use the Table of Integrals on Reference Pages 6–10 to evaluate the integral. Transcribed Image Text: sec?0 tan?0 de 9 – tan20
Answer Preview: Let utan 0 and a 3 Then d…
, Chapter: 2 -Problem: 50 >> The table shows values of the viral load V(t) in HIV patient 303, measured in RNA copies/mL, t days after ABT-538 treatment was begun. (a) Find the average rate of change of V with respect to t over each time interval:(i) [4, 11] (ii) [8, 11](iii) [11, 15](iv) [11, 22]What are the units?(b) Estimate and interpret the value of the derivative V?(11).
Answer Preview: a i ii iii iv b An estimate of V 11 is the average …
, Chapter: 8 -Problem: 94 >> After many nights of observation, you notice that if you oversleep one night, you tend to undersleep the following night, and vice versa. This pattern of compensation is described by the relationship where xn is the number of hours of sleep you get on the nth night and x0 = 7 and x1 = 6 are the number of hours of sleep on the first two nights, respectively. a. Write out the first six terms of the
Answer Preview: a. Io = 7, x = 6, x = 6 5 = 12, x3 = 6 25, x = 6 375 = 5,5 = 6 3125 = 101, x6 =6 34375 = 203 b…
, Chapter: 15 -Problem: 32 >> Calculate the double integral. Transcribed Image Text: R=[0, 1] × [0, 1] -dA, 1+ ??
Answer Preview: 6 fx sin x y dy dx 6 x cos x y 7 d…
, Chapter: 14 -Problem: 34 >> Find the first partial derivatives of the function.w = y tan(x + 2z)
Answer Preview: aw w y tan x 2 y …
, Chapter: 15 -Problem: 51 >> The joint density function for random variables X, Y, and Z is f (x, y, z) = Cxyz if 0 < x < 2, 0 < y < 2, 0 < z < 2, and f (x, y, z) = 0 otherwise. (a) Find the value of the constant C. (b) Find P(X < 1, Y < 1, Z < 1). (c) Find P(X + Y + Z < 1).
Answer Preview: a f x y z is a joint density function so we know fff x y z dV 1 …
, Chapter: 10 -Problem: 9 >> Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.The graph of y2 = 2y + 3x is a parabola.
Answer Preview: True. which is the equatio…
, Chapter: 11 -Problem: 24 >> Test the series for convergence or divergence. Transcribed Image Text: En sin(1/n) n=1
Answer Preview: lim an lim 11 00 11 00 n s…
, Chapter: 3 -Problem: 3 >> A bacteria culture initially contains 100 cells and grows at a rate proportional to its size. After an hour the population has increased to 420. (a) Find an expression for the number of bacteria after t hours. (b) Find the number of bacteria after 3 hours. (c) Find the rate of growth after 3 hours. (d) When will the population reach 10,000?
Answer Preview: a b c d By Theorem 2 …
, Chapter: 18 -Problem: 32 >> Find polar forms for zw, z/w, and 1/z by first putting z and w into polar form.z = 4(?3 + i), w = -3 - 3i
Answer Preview: For z 4 3 i 43 4i r 43 4 64 8 and tan 0 V …
, Chapter: 11 -Problem: 16 >> (a) Approximate f by a Taylor polynomial with degree n at the number a. (b) Use Taylor's Inequality to estimate the accuracy of the approximation f(x) ? Tn (x) when x line in the given interval. (c) Check your result in part (b) by graphing |Rn (x)|. Transcribed Image Text: f(x) — sin x, a — ?/6, ?
Answer Preview: 22 C 0 1 2 3 f n x f n 6 s…
, Chapter: 16 -Problem: 20 >> If F and G are vector fields whose component functions have continuous first partial derivatives, show that curl(F x G) = F div G - G div F + (G • ?)F - (F • ?)G
Answer Preview: Let F P1 i Q1 j R1 k and G Pz i Qzj R2 k be vector fields whose …
, Chapter: 1 -Problem: 39 >> Find f ? g ? h.f(x) = 3x – 2, g(x) = sinx, h(x) = x2
Answer Preview: f g h x f…
, Chapter: 3 -Problem: 11 >> Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement. The derivative of a polynomial is a polynomial.
Answer Preview: True If which is …
, Chapter: 10 -Problem: 10 >> (a) Sketch the curve by using the parametric equations to plot points. Indicate with an arrow the direction in which the curve is traced as t increases. (b) Eliminate the parameter to find a Cartesian equation of the curve.x = t2, y = t3
Answer Preview: x t y t a t X Y b y t 2 …
, Chapter: 12 -Problem: 34 >> Identify and sketch the graph of each surface.y2 + z2 ? 1 + x2
Answer Preview: An equivalent a …
, Chapter: 15 -Problem: 42 >> Find the volume of the solid in the first octant bounded by the cylinder z = 16 - x2 and the plane y = 5.
Answer Preview: The cylinder intersects the xy plane along t…
, Chapter: 3 -Problem: 46 >> A Ferris wheel with a radius of 10 m is rotating at a rate of one revolution every 2 minutes. How fast is a rider rising when his seat is 16 m above ground level?
Answer Preview: We are given th…
, Chapter: 16 -Problem: 12 >> (a) Find a function f such that F = ?f and (b) use part (a) to evaluate ?C F • dr along the given curve C. Transcribed Image Text: F(x, y) = (3 + 2xy³) i + 2x²yj, Cis the arc of the hyperbola y = 1/x from (1, 1) to (4,)
Answer Preview: a If F V then x x y 3 2xy …
, Chapter: 10 -Problem: 35 >> Sketch the curve with the given polar equation by first sketching the graph of r as a function of ? in Cartesian coordinates.r = 3 cos 3?
Answer Preview: r 3 c…
, Chapter: 12 -Problem: 7 >> Write expressions for the scalar and vector projections of b onto a. Illustrate with diagrams.
Answer Preview: The scalar projection of a vector b onto a vector a is given by b a a a a where denotes t…
, Chapter: 14 -Problem: 17 >> Find the first partial derivatives of the function.f (x, t) = t2e-x
Answer Preview: f x t …
, Chapter: 16 -Problem: 25 >> Evaluate the surface integral ??S F • dS for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation.F(x, y, z) = x i + y j + z2 k, S is the sphere with radius 1 and center the origin
Answer Preview: F x y z xi yj z k and using spherical coordinates S is given by x sin cos …
, Chapter: 4 -Problem: 39 >> Find f. f''(x) = - 2 + 12x - 12x2, f(0) = 4, f' (0) = 12
Answer Preview: f x 2 12x12x f x 2x 6x 4x C …
, Chapter: 7 -Problem: 50 >> Show that 1/3 (Tn + 2/3Mn) S2n.
Answer Preview: Since are the subinterval endpoints for S 2n and since In …
, Chapter: 3 -Problem: 58 >> Find the derivative of the function. Simplify where possible.y = cos-1(sin-1 t)
Answer Preview: y cos si…
, Chapter: 9 -Problem: 53 >> Write the Taylor series for f(x) = ln (1 + x) about 0 and find its interval of convergence. Assume the Taylor series converges to f on the interval of convergence. Evaluate f(1) to find the value of (the alternating harmonic series). Transcribed Image Text: k=1 (?1)k+1 k
Answer Preview: We have e-2 = 1 - x + /2 - 1…
, Chapter: 14 -Problem: 2 >> (a) Use a graphing calculator or computer to graph the circle x2 + y2 = 1. On the same screen, graph several curves of the form x2 + y = c until you find two that just touch the circle. What is the significance of the values of c for these two curves? (b) Use Lagrange multipliers to find the extreme values of f (x, y) = x2 + y subject to the constraint x2 + y2 = 1. Compare your answers with those
Answer Preview: a The values c 1 and c 1 25 seem to give curves which are tangent to the circle These values repr…
, Chapter: 14 -Problem: 42 >> At the beginning of this section we considered the functionf (x, y) = sin(x2 + y2)/x2 + y2 and guessed on the basis of numerical evidence that f (x, y) ? 1 as (x, y) ? (0, 0). Use polar coordinates to confirm the value of the limit. Then graph the function.
Answer Preview: sin x y 29 0 0 x y lim sin 2 H lim r 0 p…
, Chapter: 15 -Problem: 31 >> When studying the formation of mountain ranges, geologists estimate the amount of work required to lift a mountain from sea level. Consider a mountain that is essentially in the shape of a right circular cone. Suppose that the weight density of the material in the vicinity of a point P is g(P) and the height is h(P). (a) Find a definite integral that represents the total work done in forming the m
Answer Preview: a The mountain comprises a solid conical region C The wor…
, Chapter: 10 -Problem: 10 >> Find an equation of the parabola. Then find the focus and directrix. Transcribed Image Text: y. 0 -1 2 X
Answer Preview: The vertex is (2, 2), so the equation is of the form …
, Chapter: 11 -Problem: 32 >> For what values of p is each series convergent? Transcribed Image Text: (-1)"-1 ? ?? ?-1 ?-1
Answer Preview: If p 0 1 n 1 If p 0 lim 11 00 converges n 1 …
, Chapter: 3 -Problem: 16 >> Differentiate the function.y = ln |1 + t - t3|
Answer Preview: y ln 1 t …
, Chapter: 18 -Problem: 42 >> Prove the identity.cos (?/2 - x) = sin x
Answer Preview: Given that cos 2 x sin x We kn…
, Chapter: 12 -Problem: 48 >> Find an equation for the surface consisting of all points P for which the distance from P to the x-axis is twice the distance from P to the yz-plane. Identify the surface.
Answer Preview: Let P x y z be an arbitrary point whose distance from the x axi…
, Chapter: 16 -Problem: 6 >> Evaluate the line integral.?C ?xy dx + ey dy + xz dz, C is given by r(t) = t4 i + t2 j + t3 k, 0 < t < 1
Answer Preview: Sc xy dx e dy x…
, Chapter: 1 -Problem: 24 >> Find a formula for the inverse of the function.y = x2 – x, ? 1/2
Answer Preview: y f x x 2 x x 1 2 y x 2 …
, Chapter: 3 -Problem: 6 >> Find the numerical value of each expression.(a) sinh 1 (b) sinh-1 1
Answer Preview: a b Usi…
, Chapter: 10 -Problem: 4 >> Find the area of the region that is bounded by the given curve and lies in the specified sector. Transcribed Image Text: r%3D 1/0, ?/2 <0<2m ?/2 <0< 2?
Answer Preview: A J J…
, Chapter: 16 -Problem: 11 >> Use Green’s Theorem to evaluate ?C F • dr. (Check the orientation of the curve before applying the theorem.)F(x, y) = (y cos x - xy sin x, xy + x cos x), C is the triangle from (0, 0) to (0, 4) to (2, 0) to (0, 0)
Answer Preview: F x y y cos x xy sinx xy x cos x and the region D enclosed by C is given …
, Chapter: 12 -Problem: 7 >> Describe and sketch the surface.xy = 1
Answer Preview: Since z is missing each horizontal t…
, Chapter: 15 -Problem: 53 >> Evaluate the integral by reversing the order of integration. Transcribed Image Text: Vy3 + 1 dy dx
Answer Preview: 0 1 0 y 1 y x or …
, Chapter: 3 -Problem: 50 >> Let P(x) ? F(x)G(x) and Q(x) ? F(x)yG(x), where F and G are the functions whose graphs are shown. (a) Find P'(2).(b) Find Q'(7). Transcribed Image Text: F1
Answer Preview: a b P x F …
, Chapter: 16 -Problem: 11 >> Evaluate the line integral, where C is the given curve.?C xeyz ds, C is the line segment from (0, 0, 0) to (1, 2, 3)
Answer Preview: Parametric equations for …
, Chapter: 10 -Problem: 1 >> Plot the point whose polar coordinates are given. Then find two other pairs of polar coordinates of this point, one with r > 0 and one with r > 0.(a) (1, ?/4) (b) (-2, 3?/2) (c) (3, 2/3)
Answer Preview: a 1 7 b 2 3 c 3 1 7 37 0 2 37 33 3 By adding 2 …
, Chapter: 13 -Problem: 8 >> A cable has radius r and length L and is wound around a spool with radius R without over-lapping. What is the shortest length along the spool that is covered by the cable?
Answer Preview: let us assume N number of turns of cable of radius r are ma…
, Chapter: 14 -Problem: 10 >> Evaluate the limit or show that it does not exist. Transcribed Image Text: 2xy lim (x, y)?(0, 0) x² + 2y?
Answer Preview: As x y 0 0 along the x axis x …
, Chapter: 16 -Problem: 55 >> (a) Use the Midpoint Rule for double integrals (see Section 15.1) with six squares to estimate the area of the surface z = 1/(1 + x2 + y2), 0 < x < 6, 0 < y < 4.(b) Use a computer algebra system to approximate the surface area in part (a) to four decimal places. Compare with the answer to part (a).
Answer Preview: 2 2 z z 4x 4y 1 SS S 1 dA 1 1 x y 4 a A S Using the Midpoin…
, Chapter: 4 -Problem: 48 >> Use the guidelines of this section to sketch the curve. y = ex/x2
Answer Preview: y f x e x A D 0 0 U 0 B No intercept C No symmetry D lim m lim 0 2 0 50 x 0 is …
, Chapter: 7 -Problem: 40 >> Use a computer algebra system to evaluate the integral. Compare the answer with the result of using tables. If the answers are not the same, show that they are equivalent. Transcribed Image Text: cos*x dx
Answer Preview: Derive gives dx ex 3ex 2 Mathematica gives 1 ex 3ex 2 3 ln 3e 2 4 3 …
, Chapter: 3 -Problem: 61 >> Find an equation of the normal line to the curve y = ?x that is parallel to the line 2x + y = 1.
Answer Preview: The slope of y x is given by The slope of 2x y 1 or y …
, Chapter: 8 -Problem: 100 >> For a positive real number p, the tower of exponents ppp a continues indefinitely and the expression is ambiguous. The tower could be built from the top as the limit of the sequence {pp, (pp)p, ((pp)p)p, . . .}, in which case the sequence is defined recursively asan + 1 = apn (building from the top, (1)where a1 = pp. The tower could also be built from th
Answer Preview: a. With p = 0 5 we have for an+1 = b. With p = 1 2 and an n an n Experi…
, Chapter: 15 -Problem: 35 >> Sketch the solid whose volume is given by the iterated integral. Transcribed Image Text: (4 - x - 2y) dx dy
Answer Preview: z f x y 4x 2y 0 for 0 x 1 an…
, Chapter: 14 -Problem: 73 >> Use the table of values of f (x, y) to estimate the values of fx(3, 2), fx(3, 2.2), and fxy(3, 2). Transcribed Image Text: 1.8 2.0 2.2 2.5 12.5 10.2 9.3 18.1 3.0 17.5 15.9 3.5 26.1 20.0 22.4
Answer Preview: By Definition 4 f 3 2 lim A 0 fa 3 2 3 5 2 f 3 2 0 5 fa 3 2 2 3 h 2 3 2 h f 3 1 8 22 4 17 5 0 5 thes…
, Chapter: 15 -Problem: 18 >> Use cylindrical coordinates.Evaluatewhere E is enclosed by the paraboloid z = x2 + y2 and the plane z = 4. Transcribed Image Text: AP SIIE z dV,
Answer Preview: The paraboloid z x y r intersects the plane z 4 …
, Chapter: 11 -Problem: 17 >> Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.If an > 0 and ?an converges, then ?(–1)nan converges.
Answer Preview: True by Theorem …
, Chapter: 11 -Problem: 8 >> Use the Ratio Test to determine whether the series is convergent or divergent. Transcribed Image Text: (-2)" ? ?? 00 ?-1
Answer Preview: an 1 lim 12180 an 2 n 1 72 …
, Chapter: 3 -Problem: 1 >> Explain why the natural logarithmic function y = ln x is used much more frequently in calculus than the other logarithmic functions y = logb x.
Answer Preview: The differentiation f…
, Chapter: 18 -Problem: 36 >> Find the indicated power using De Moivre’s Theorem. (1 - i)8
Answer Preview: This will give us the power 8i From this the power of the other terms and the…
, Chapter: 13 -Problem: 3 >> Find the length of the curve.r(t) = ?2 t i + et j + e-t k, 0 < t < 1
Answer Preview: r t 2ti ej e k r t 2…
, Chapter: 16 -Problem: 11 >> Use the Divergence Theorem to calculate the surface integral ??S F • dS; that is, calculate the flux of F across S.F(x, y, z) = (2x3 + y3) i + (y3 + z3) j + 3y2z k, S is the surface of the solid bounded by the paraboloid z = 1 - x2 - y2 and the xy-plane
Answer Preview: div F 6x 3y 3y 6x 6y …
, Chapter: 1 -Problem: 35 >> Find the functions(a) f° g,(b) g°f,(c) f°f, and(d) g°gand their domains.f(x) = ?x + 1, g(x) = 4x – 3
Answer Preview: a The domain of …
, Chapter: 4 -Problem: 4 >> The sum of two positive numbers is 16. What is the smallest possible value of the sum of their squares?
Answer Preview: Call the two numb…
, Chapter: 10 -Problem: 43 >> Sketch the curve with the given polar equation by first sketching the graph of r as a function of ? in Cartesian coordinates.r = 2 + sin 3?
Answer Preview: r 2 sin …
, Chapter: 4 -Problem: 30 >> Use the guidelines of Section 4.5 to sketch the curve.y = 4x - tan x, -?/2 < x < ?/2
Answer Preview: sinx 0 y f x e sinx x A D B y i…
, Chapter: 12 -Problem: 11 >> Use traces to sketch and identify the surface.x = y2 + 4z2
Answer Preview: For x y 42 the traces in a k are y 4x k Whenk 0 we have a family of ellipses When k 0 …
, Chapter: 15 -Problem: 7 >> Evaluate the double integral. Transcribed Image Text: - dA, D= {(x, y) | 0 < x< 4,0 < y< /x} x? + 1
Answer Preview: x ff 5 mp4 …
, Chapter: 9 -Problem: 14 >> Find the solution of the differential equation that satisfies the given initial condition. x + 3y2 ?x2 + 1 dy/dx = 0, y = (0) = 1
Answer Preview: x 3y dy 1 f3y dy f x …
, Chapter: 3 -Problem: 54 >> A model for the velocity of a falling object after time t is where m is the mass of the object, g = 9.8 m/s2 is the acceleration due to gravity, k is a constant, t is measured in seconds, and v in mys. (a) Calculate the terminal velocity of the object, that is, limt? ?(t). (b) If a person falls from a building, the value of the constant k depends on his or her position. For a “belly-to-earth” posi
Answer Preview: a b mg gk mg mg …
, Chapter: 16 -Problem: 17 >> (a) Find a function f such that F = ?f and (b) use part (a) to evaluate ?C F • dr along the given curve C.F(x, y, z) = yzexz i + exz j + xyexz k, C: r(t) = (t2 + 1) i + (t2 - 1) j + (t2 - 2t) k, 0 < t < 2
Answer Preview: a fx x y z yze implies f x y z ye z g y z and so fy …
, Chapter: 11 -Problem: 23 >> Determine whether the series is convergent or divergent. Transcribed Image Text: ? kek k=1
Answer Preview: The function f x xe f x Sx e l xe e 1 x e xe so the series ke k …
, Chapter: 18 -Problem: 85 >> Use the figure to prove the subtraction formula cos(a - B) = cos a cos B + sin a sin B Compute c2 in two ways (using the Law of Cosines from Exercise 83 and also using the distance formula) and compare the two expressions.]
Answer Preview: In AOB AOB Apply the Law of cosine in AOB cos 1 2 1 2 c 2 2 …
, Chapter: 14 -Problem: 7 >> Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.If f has a local minimum at (a, b) and f is differentiable at (a, b), then ?f (a, b) = 0.
Answer Preview: True If f has a local mini…
, Chapter: 16 -Problem: 60 >> (a) Show that the parametric equations x = a cosh u cos v, y = b cosh u sin v, z = c sinh u, represent a hyperboloid of one sheet. (b) Use the parametric equations in part (a) to graph the hyperboloid for the case a = 1, b = 2, c = 3. (c) Set up, but do not evaluate, a double integral for the surface area of the part of the hyperboloid in part (b) that lies between the planes z = -3 and z = 3.
Answer Preview: a x a cosh u cos v y bcosh u sin v z c sinh u z cosh u …
, Chapter: 4 -Problem: 49 >> Given that the graph of f passes through the point (2, 5) and that the slope of its tangent line at (x, f(x)) is 3 - 4x, find f (1).
Answer Preview: The slope of its tangent li…
, Chapter: 7 -Problem: 13 >> Use the Table of Integrals on Reference Pages 6–10 to evaluate the integral. Transcribed Image Text: arctan Vx dx
Answer Preview: s arctan v x far 8…
, Chapter: 2 -Problem: 38 >> Water temperature affects the growth rate of brook trout. The table shows the amount of weight gained by brook trout after 24 days in various water temperatures.Temperature (°C) Weight gained (g)15.5.........................................................37.217.7.........................................................31.020.0................................................
Answer Preview: We use one sided difference quotients for the firs…
, Chapter: 8 -Problem: 94 >> Suppose a function f is defined by the geometric series a. Evaluate f(0), f(0.2), f(0.5), f(1), and f(1.5), if possible. b. What is the domain of f ? Transcribed Image Text: f(x) = Co x k k=0
Answer Preview: a. f(x) = = ; because is represented by a …
, Chapter: 5 -Problem: 10 >> Evaluate the indefinite integral. Transcribed Image Text: | sint /1 + cost dt
Answer Preview: Let u 1 cost Then …
, Chapter: 14 -Problem: 35 >> Use Lagrange multipliers to give an alternate solutionFind three positive numbers whose sum is 100 and whose product is a maximum.
Answer Preview: f x y z xyz g x …
, Chapter: 14 -Problem: 54 >> Find all the second partial derivatives. f (x, y) = ln(ax + by)
Answer Preview: f x y ln ax by fz x y fax x y a ax …
, Chapter: 15 -Problem: 39 >> Use cylindrical or spherical coordinates, whichever seems more appropriate.where E lies above the paraboloid z = x2 + y2 and below the plane z = 2y. Use either the Table of Integrals (on Reference Pages 6–10) or a computer algebra system to evaluate the integral. Transcribed Image Text: Evaluate [[e
Answer Preview: In cylindrical coordinates the paraboloid is …
, Chapter: 10 -Problem: 7 >> Write a polar equation of a conic with the focus at the origin and the given data.Parabola, vertex (3, ?/2)
Answer Preview: The vertex (3, /2) is 3 units above the focus at …
, Chapter: 11 -Problem: 10 >> Test the series for convergence or divergence. Transcribed Image Text: ?nen ,3 n=1
Answer Preview: Let f x x e Then f is continuous and positi…
, Chapter: 18 -Problem: 62 >> If sin x = 1/3 and sec y = 5/4, where x and y lie between 0 and ?/2, evaluate the expression.sin(x - y)
Answer Preview: Given that sin x 1 3 sec y 5 4 where x and y lie …
, Chapter: 12 -Problem: 49 >> Prove that (a - b) x (a + b) = 2(a x b).
Answer Preview: a b x a b a b xa a b x b aXa b Xa axb …
, Chapter: 16 -Problem: 17 >> A particle moves along line segments from the origin to the points (1, 0, 0), (1, 2, 1), (0, 2, 1), and back to the origin under the influence of the force field F(x, y, z) = z2 i + 2xy j + 4y2 k Find the work done.
Answer Preview: It is easier to use Stokes Theorem than to compute the work d…
, Chapter: 1 -Problem: 53 >> Find an expression for the function whose graph is the given curve. The bottom half of the parabola x + (y – 1)2 = 0
Answer Preview: We need to solve the given equation for y x y 1 2 0 y …
, Chapter: 4 -Problem: 3 >> For each of the numbers a, b, c, d, r, and s, state whether the function whose graph is shown has an absolute maximum or minimum, a local maximum or minimum, or neither a maximum nor a minimum. Transcribed Image Text: ?? c dr ?
Answer Preview: Absolute maximum at s abs…
, Chapter: 10 -Problem: 2 >> Sketch the curve by using the parametric equations to plot points. Indicate with an arrow the direction in which the curve is traced as t increases. Transcribed Image Text: .3 .2 x = t° + t, y = t² + 2, -2 < t< 2 %3D
Answer Preview: x t t y t 2 2 t 2 …
, Chapter: 5 -Problem: 4 >> Let g(x) = ? x0 f (g) dt, where f is the function whose graph is shown. (a) Evaluate g(0) and g(6). (b) Estimate t(x) for x = 1, 2, 3, 4, and 5. (c) On what interval is t increasing? (d) Where does t have a maximum value? (e) Sketch a rough graph of g. (f) Use the graph in part (e) to sketch the graph of g'(x). Compare with the graph of f.
Answer Preview: a so g 0 0 since the limits of integration are equal and g 6 0 since the areas a…
, Chapter: 13 -Problem: 2 >> Find the domain of the vector function. r(t) = cos t i + ln t j + 1/t - 2k
Answer Preview: The component functio…
, Chapter: 15 -Problem: 22 >> Evaluate the double integral.D is the triangular region with vertices (0, 0), (1, 1), and (4, 0) Transcribed Image Text: || y dA,
Answer Preview: 0 x y 1 1 D y x x 4 3…
, Chapter: 18 -Problem: 19 >> Solve the inequality in terms of intervals and illustrate the solution set on the real number line.-1 < 2x - 5 < 7
Answer Preview: 1 2x 5 …
, Chapter: 3 -Problem: 15 >> (a) Find the differential dy and (b) Evaluate dy for the given values of x and dx.y = ex/10, x = 0, dx = 0.1
Answer Preview: a b xP xp OT 10 xp 01 x …
, Chapter: 16 -Problem: 22 >> Suppose an experiment determines that the amount of work required for a force field F to move a particle from the point (1, 2) to the point (5, -3) along a curve C1 is 1.2 J and the work done by F in moving the particle along another curve C2 between the same two points is 1.4 J. What can you say about F? Why?
Answer Preview: The curves C and C connect …
, Chapter: 11 -Problem: 2 >> Test the series for convergence or divergence. Transcribed Image Text: 2 11 3
Answer Preview: 2 2 1 2 1 1 1 n 1 series …
, Chapter: 14 -Problem: 16 >> (a) If f has a local maximum at (a, b), what can you say about its partial derivatives at (a, b)? (b) What is a critical point of f ?
Answer Preview: Ans a Let me fist give you the answer then explanation f has a local maximum at a b then its partial …
, Chapter: 14 -Problem: 25 >> Find equations of (a) The tangent plane and (b) The normal line to the given surface at the specified point.z = 3x2 - y2 + 2x, (1, -2, 1)
Answer Preview: a x 6x 2 Z 1 2 8 and y 2y zy 1 2 4 so an equation of the ta…
, Chapter: 16 -Problem: 13 >> Evaluate the surface integral.??S z2 dS, S is the part of the paraboloid x = y2 + z2 given by 0 < x < 1
Answer Preview: Using y and z as parameters we have r y z y z i yj zk y z …
, Chapter: 4 -Problem: 54 >> Find the limit. Use 1’Hospital’s Rule where appropriate. If there is a more elementary method, consider using it. If 1’Hospital’s Rule doesn’t apply, explain why. Transcribed Image Text: lim tan tan ? ?
Answer Preview: This limit has the form lim 2 0 tan x l…
, Chapter: 7 -Problem: 21 >> Use the Table of Integrals on Reference Pages 6–10 to evaluate the integral. Transcribed Image Text: e* dx 3 – e2x
Answer Preview: Let ue and a 3 Then …
, Chapter: 2 -Problem: 36 >> Find f ?(a).f (x) = 4/?1 - x
Answer Preview: Use 4 with f x 4 1 x f a lim h0 f a h f a h 4 lim 0 lim h0 1 a 1 a h 1 a …
, Chapter: 8 -Problem: 108 >> In the following exercises, two sequences are given, one of which initially has smaller values, but eventually “overtakes” the other sequence. Find the sequence with the larger growth rate and the value of n at which it overtakes the other sequence.an = n1.001 and bn = ln n10, n ? 1
Answer Preview: By Theorem 8 6, Inn0n 001, so that n…
, Chapter: 5 -Problem: 10 >> Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. Transcribed Image Text: n. h(u) = " dt Jo t + 1
Answer Preview: f t 7 t 1 …
, Chapter: 14 -Problem: 7 >> Each of these extreme value problems has a solution with both a maximum value and a minimum value. Use Lagrange multipliers to find the extreme values of the function subject to the given constraint.f (x, y, z) = 2x + 2y + z; x2 + y2 + z2 = 9
Answer Preview: f x y z 2x 2y z g x y z x y z 9 and V XVg andz 2xy 2 2Az 1 and x y …
, Chapter: 14 -Problem: 53 >> Find all the second partial derivatives.f (x, y) = x4y - 2x3y2
Answer Preview: f x y xy 2xy fx x y 4…
, Chapter: 15 -Problem: 15 >> A solid lies above the cone z = ?x2 + y2 and below the sphere x2 + y2 + z2 = z. Write a description of the solid in terms of inequalities involving spherical coordinates.
Answer Preview: x y because the solid lies above the cone Squaring both sides of this inequality …
, Chapter: 10 -Problem: 12 >> Match the polar equations with the graphs labeled I–VI. Give reasons for your answer. Transcribed Image Text: * III II ? IV VI --------- 3
Answer Preview: where e = 3/4 < 1, so the coni…
, Chapter: 11 -Problem: 11 >> Test the series for convergence or divergence. Transcribed Image Text: n? n+1 3 n' + 4 n=1
Answer Preview: bn n 4 0 for n 1 b is decreasing for n 2 …
, Chapter: 3 -Problem: 20 >> Evaluate Transcribed Image Text: + x)? – sin 9 sin(3 lim
Answer Preview: lim x 0 sin 3 …
, Chapter: 18 -Problem: 69 >> Find all values of x in the interval [0, 2?] that satisfy the equation.sin 2x = cos x
Answer Preview: Using 15a we have sin 2x co…
, Chapter: 12 -Problem: 44 >> Sketch the region bounded by the paraboloids z = x2 + y2 and z = 2 - x2 - y2.
Answer Preview: N 0…
, Chapter: 16 -Problem: 14 >> Use the Divergence Theorem to calculate the surface integral ??S F • dS; that is, calculate the flux of F across S.F = |r|2 r, where r = x i + y j + z k, S is the sphere with radius R and center the origin
Answer Preview: F x y z x x y x i y x y x j z x y x k …
, Chapter: 1 -Problem: 64 >> Find the exact value of each expression.(a) tan–1( – 1)(b) arctan(–1)
Answer Preview: a tan 1 3 3 because tan 3 3 an…
, Chapter: 3 -Problem: 2 >> Find the numerical value of each expression.(a) tanh 0 (b) tanh 1
Answer Preview: a b …
, Chapter: 10 -Problem: 14 >> (a) Eliminate the parameter to find a Cartesian equation of the curve. (b) Sketch the curve and indicate with an arrow the direction in which the curve is traced as the parameter increases. x = et, y = e-2t
Answer Preview: a y e e…
, Chapter: 16 -Problem: 16 >> Verify Green’s Theorem by using a computer algebra system to evaluate both the line integral and the double integral.P(x, y) = 2x - x3y5, Q(x, y) = x3y8, C is the ellipse 4x2 + y2 = 4
Answer Preview: We can parametrize C as x cos 0 y 2 sin 0 00 2 Then the …
, Chapter: 12 -Problem: 9 >> (a) Find and identify the traces of the quadric surface x2 + y2 - z2 = 1 and explain why the graph looks like the graph of the hyperboloid of one sheet in Table 1. (b) If we change the equation in part (a) to x2 - y2 + z2 = 1, how is the graph affected? (c) What if we change the equation in part (a) to x2 + y2 + 2y - z2 = 0?
Answer Preview: a The traces of x y 2 1 in x k are y z 1 k a family of hyperbolas Note that the …
, Chapter: 15 -Problem: 48 >> Sketch the region of integration and change the order of integration. Transcribed Image Text: V4-y2 f(x, y) dx dy |-2 Jo
Answer Preview: N 2 x y 4 X Because the re…
, Chapter: 7 -Problem: 55 >> Use Exercise 51 to find ? (ln x)3 dx.
Answer Preview: By repeated applications of the reduction …
, Chapter: 3 -Problem: 45 >> Find an equation of the tangent line to the hyperbolaat the point (x0, y0). so the four points are Transcribed Image Text: y? b2 .2 and y? = 75 25 16 16
Answer Preview: an equation of the tangent …
, Chapter: 16 -Problem: 34 >> At time t = 1, a particle is located at position (1, 3). If it moves in a velocity fieldF(x, y) = (xy - 2, y2 - 10) find its approximate location at time t = 1.05.
Answer Preview: At t 1 the particle is at 1 3 so its velocity …
, Chapter: 9 -Problem: 5 >> Solve the differential equation.(ey - 1) y' = 2 + cos x
Answer Preview: e 1 y 2 cos x e 1 f e 1 …
,
, Chapter: 14 -Problem: 85 >> Show that the Cobb-Douglas production function satisfies P(L, K0) = C1(K0)Lby solving the differential equationdP/dL = a P/L
Answer Preview: dP If we fix K Ko P L Ko is a function of a single varia…
, Chapter: 16 -Problem: 1 >> Let S be the surface of the box enclosed by the planes x = ±1, y = ±1, z = ±1. Approximate ??S cos(x + 2y + 3z) dS by using a Riemann sum as in Definition 1, taking the patches Sij to be the squares that are the faces of the box S and the points Pij* to be the centers of the squares.
Answer Preview: The box is a cube where each face has surface area 4 The cente…
, Chapter: 7 -Problem: 78 >> Evaluate the integral. Transcribed Image Text: 1 + sin x 1- sin x
Answer Preview: Thus 1 sin x 1 sin x 2 sin x sin x 1 sin …
, Chapter: 3 -Problem: 57 >> Find an equation of the tangent to the curve at the given point.y = 4 sin2x, (?/6, 1)
Answer Preview: y 4sinx y 4 2 sin x c…
, Chapter: 8 -Problem: 101 >> The famous Fibonacci sequence was proposed by Leonardo Pisano, also known as Fibonacci, in about a.d. 1200 as a model for the growth of rabbit populations. It is given by the recurrence relation fn + 1 = fn + fn - 1, for n = 1, 2, 3,? . . ., where f0 = 1, f1 = 1. Each term of the sequence is the sum of its two predecessors.? a. Write out the first ten terms of the sequence. b. Is the sequence boun
Answer Preview: a. fo = f = 1, f = 2, f3 = 3, f = 5, f5 = 8, f6 = 13, f7 = …
, Chapter: 14 -Problem: 48 >> Find the dimensions of the box with volume 1000 cm3 that has minimal surface area.
Answer Preview: Let x y and z be the dimensions of the box We wish to minimize surface area 2xy 2xz 2yz but we hav…
, Chapter: 15 -Problem: 14 >> Use a graphing device to draw the solid enclosed by the paraboloids z = x2 + y2 and z = 5 - x2 - y2.
Answer Preview: In cylindrical coordinates the equations are z r and z 5 r The …
, Chapter: 10 -Problem: 19 >> Find a polar equation for the curve represented by the given Cartesian equation.x + y = 2
Answer Preview: x+y=2 r cos 0 …
, Chapter: 11 -Problem: 4 >> Determine whether the series is absolutely convergent or conditionally convergent. Transcribed Image Text: (-1)" n° + 1 .3 n-1
Answer Preview: 0 …
, Chapter: 7 -Problem: 18 >> Evaluate the integral. Transcribed Image Text: sin x cos(x) dx
Answer Preview: s x dx f sin 2 x co…
, Chapter: 3 -Problem: 20 >> Differentiate.y = (z2 + ez)?z
Answer Preview: y 2 e z PR y y …
, Chapter: 11 -Problem: 4 >> Find the Taylor polynomial T3(x) for the function f centered at the number a. Graph f and T3 on the same screen.f (x) = sin x, a = ?/6
Answer Preview: 22 0 1 2 3 f n x f n 6 sin x …
, Chapter: 3 -Problem: 6 >> Write the composite function in the form f ( g(x)). [Identify the inner function u = t(x) and the outer function y = f (u).] Then find the derivative dy/dx.y = ?2 - ex
Answer Preview: Let dy u g x …
, Chapter: 1 -Problem: 23 >> Graph the function by hand, not by plotting points, but by starting with the graph of one of the standard functions given in Section 1.2, and then applying the appropriate transformations.y = |?x – 1|
Answer Preview: y x 1 Start with the graph of y …
, Chapter: 10 -Problem: 14 >> Graph the curve and find the area that it encloses.r = 3 - 2 cos 4?
Answer Preview: A 4 tr as 3 200s 48 de 9 12c…
, Chapter: 12 -Problem: 28 >> Identify and sketch the graph of each surface. x = 3
Answer Preview: The equation x 3 r…
, Chapter: 15 -Problem: 49 >> Sketch the region of integration and change the order of integration. Transcribed Image Text: 2 (In x f(x, y) dy dx 1
Answer Preview: In 2 y lnx or x e 1 y 0 x 2 2 x Bec…
, Chapter: 18 -Problem: 5 >> Rewrite the expression without using the absolute-value symbol.|?5 - 5|
Answer Preview: 5 5 5…
, Chapter: 3 -Problem: 44 >> Suppose that f (4) = 2, g(4) = 5, f'(4) = 6, and g'(4) = - 3. Find h'(4).(a) h(x) = 3f (x) + 8g(x)(b) h(x) = f (x) g(x)(c) h(x) = f (x) g(x)(d) h(x) = g(x) f (x) + g(x)
Answer Preview: We are giv…
, Chapter: 16 -Problem: 23 >> Find the work done by the force field F in moving an object from P to Q.F(x, y) = x3 i + y3 j; P(1, 0), Q(2, 2)
Answer Preview: F x y xi yj W F dr Since x y 0 y ax ther…
, Chapter: 10 -Problem: 26 >> Find a polar equation for the curve represented by the given Cartesian equation.x2 - y2 = 4
Answer Preview: x y 4 r cos …
, Chapter: 18 -Problem: 76 >> Find all values of x in the interval [0, 2?] that satisfy the inequality.sin x > cos x
Answer Preview: Solution x 2 0 x 0 2 x 2 x 3 2 x 3 2 2 Answer 2 3 and 1 5 The following inequalities are i…
, Chapter: 14 -Problem: 15 >> Find the first partial derivatives.F(a, B) = a2 ln(a2 + 2)
Answer Preview: F a a In a 3 FB …
, Chapter: 16 -Problem: 33 >> Find an equation of the tangent plane to the given parametric surface at the specified point.x = u + v, y = 3u2, z = u - v; (2, 3, 0)
Answer Preview: r u v u v i 3u j u v k r i Guj k and r i k s…
, Chapter: 7 -Problem: 27 >> Determine whether each integral is convergent or divergent. Evaluate those that are convergent. Transcribed Image Text: -dx ?? ? ? J0
Answer Preview: S da x lim …
, Chapter: 3 -Problem: 66 >> Find the points on the ellipse x2 + 2y2 = 1 where the tangent line has slope 1.
Answer Preview: The slope of t…
, Chapter: 8 -Problem: 85 >> Evaluate the limit of the following sequences or state that the limit does not exist. Transcribed Image Text: An n 7" 7 n 5n in
Answer Preview: We can wri…
, Chapter: 14 -Problem: 49 >> Find the volume of the largest rectangular box in the first octant with three faces in the coordinate planes and one vertex in the plane x + 2y + 3z = 6.
Answer Preview: Maximize f x y 6 x 2y then the maximum volume …
, Chapter: 15 -Problem: 4 >> Change from rectangular to spherical coordinates.(a) (1, 0, ?3)(b) (?3 , -1, 2?3)
Answer Preview: a p x y z 1 0 3 2 cos p 8 0 Thus spherical …
, Chapter: 10 -Problem: 9 >> Sketch the region in the plane consisting of points whose polar coordinates satisfy the given conditions.0 ? r ? 1, ??/2 ? ? ? ?/2
Answer Preview: 0 r 1, /2 /2. This is th…
, Chapter: 11 -Problem: 26 >> Test the series for convergence or divergence. Transcribed Image Text: n2 + 1 5" n=1
Answer Preview: an 1 n 00 an converges by …
, Chapter: 7 -Problem: 14 >> Evaluate the integral. Transcribed Image Text: sin°(1/t) dt 2
Answer Preview: sin 1 t 27 1 sin…
,
, Chapter: 12 -Problem: 33 >> Reduce the equation to one of the standard forms, classify the surface, and sketch it. x2 + 2y - 2z2 = 0
Answer Preview: x 2y 2x 0 or 2y 2…
, Chapter: 1 -Problem: 7 >> Find the domain and range of the function. Write your answer in interval notation.h(x) = ln (x + 6)
Answer Preview: h x ln x 6 Domain x …
, Chapter: 4 -Problem: 2 >> Use the guidelines of this section to sketch the curve. Transcribed Image Text: y = 2 + 3x? – x³
Answer Preview: A D R B y intercept f 0 2 C No symmet…
, Chapter: 1 -Problem: 13 >> A function is given by a table of values, a graph, a formula, or a verbal description. Determine whether it is one-to-one. f(t) is the height of a football t seconds after kickoff.
Answer Preview: A football will attain every height h …
, Chapter: 10 -Problem: 46 >> Graph the curve and find its exact length. Transcribed Image Text: T/4
Answer Preview: x cost ln tant y sint 4 t 3 4 sec t 2 tan t 2 dx dt sint …
, Chapter: 16 -Problem: 10 >> The vector field F is shown in the xy-plane and looks the same in all other horizontal planes. (In other words, F is indepen- dent of z and its z-component is 0.) (a) Is div F positive, negative, or zero? Explain. (b) Determine whether curl F = 0. If not, in which direction does curl F point? Transcribed Image Text:
Answer Preview: If the vector field isF Pi Qj Rk then we know R 0 In addition P and Q don t vary in the …
, Chapter: 12 -Problem: 35 >> Identify and sketch the graph of each surface. 4x2 + 4y2 - 8y + z2 = 0
Answer Preview: Completing the square i…
, Chapter: 15 -Problem: 4 >> Evaluate the iterated integral. Transcribed Image Text: x sin y dy dx T/2 Jo x.
Answer Preview: f f x siny dy dx f x cos …
, Chapter: 3 -Problem: 10 >> Find the derivative of the function.f (x) = 1/ 3?x2 - 1
Answer Preview: f x 1 …
, Chapter: 3 -Problem: 49 >> Calculate y'.y = cos (e?tan 3x)
Answer Preview: tan 3x y cos e y sin et…
, Chapter: 16 -Problem: 16 >> (a) Find a function f such that F = ?f and (b) use part (a) to evaluate ?C F • dr along the given curve C.F(x, y, z) = (y2z + 2xz2) i + 2xyz j + (xy2 + 2x2z) k, C: x = ?t , y = t + 1, z = t2, 0 < t < 1
Answer Preview: a fx x y z yz 2xz implies f x y z xyz xz g y z and so fy x y z 2x…
, Chapter: 9 -Problem: 3 >> Solve the differential equation.xyy' = x2 + 1
Answer Preview: x 1 ydy x 1 x xyy …
, Chapter: 16 -Problem: 11 >> (a) What is a parametric surface? What are its grid curves? (b) Write an expression for the area of a parametric surface. (c) What is the area of a surface given by an equation z = g(x, y)?
Answer Preview: a A surface by a vector function r u v is here x y …
, Chapter: 14 -Problem: 20 >> Find all second partial derivatives of f . z = xe-2y
Answer Preview: 2 xe 2y Zx…
, Chapter: 16 -Problem: 48 >> The temperature at a point in a ball with conductivity K is inversely proportional to the distance from the center of the ball. Find the rate of heat flow across a sphere S of radius a with center at the center of the ball.
Answer Preview: KVu 6 5 4yj 4z k S is given by r x 0 xi 6 …
, Chapter: 7 -Problem: 77 >> Evaluate the integral. Transcribed Image Text: ??* dx. V1 + e*
Answer Preview: Then Let y …
, Chapter: 2 -Problem: 43 >> Determine the infinite limit. Transcribed Image Text: lim (In x² – x-2)|
Answer Preview: since ln …
, Chapter: 8 -Problem: 86 >> Consider the following sequences defined by a recurrence relation. Use a calculator, analytical methods, and/or graphing to make a conjecture about the limit of the sequence or state that the sequence diverges.an + 1 = 1/2 an + 2; a0 = 5
Answer Preview: A graph shows that the sequence a…
, Chapter: 14 -Problem: 21 >> Find the extreme values of f on the region described by the inequality.f(x, y) = x2 + y2 + 4x - 4y, x2 + y2 < 9
Answer Preview: f x y x y 4x 4y For the interior of the region we find …
, Chapter: 15 -Problem: 26 >> Use cylindrical coordinates.(a) Find the volume of the solid that the cylinder r = a cos ? cuts out of the sphere of radius a centered at the origin. (b) Illustrate the solid of part (a) by graphing the sphere and the cylinder on the same screen.
Answer Preview: 2 a V S 2 S SV cos 45 4 f 2fa ST 2 sacose sva dr de r a cos S5 a …
, Chapter: 11 -Problem: 18 >> Test the series for convergence or divergence. Transcribed Image Text: (-1)"-1 ? ?? - 1 ?-2
Answer Preview: 1 n 1 n 2n 1 bn 1 for n 2 b …
, Chapter: 7 -Problem: 4 >> Evaluate the integral. Transcribed Image Text: (T/2 sin'x dx
Answer Preview: 2 f sin x dx f sin x si…
, Chapter: 3 -Problem: 20 >> If tanh x = 12/13, find the values of the other hyperbolic functions at x.
Answer Preview: 1 tanha sech x 1 tanh x 1 sech x coth x cosh x …
, Chapter: 12 -Problem: 46 >> (a) Let P be a point not on the plane that passes through the points Q, R, and S. Show that the distance d from P to the plane isd = |a • (b x c)|/|a x b|where(b) Use the formula in part (a) to find the distance from the point P(2, 1, 4) to the plane through the points Q(1, 0, 0), R(0, 2, 0), and S(0, 0, 3). Transcribed I
Answer Preview: a The distance between a point and a plane is the length of the …
, Chapter: 1 -Problem: 32 >> Find the domain of the function. Transcribed Image Text: 2x – 5 f(x) : 6. x? +? — 6
Answer Preview: f x 2x 3 5 x 2 x 6 is …
, Chapter: 3 -Problem: 12 >> A particle is moving along a hyperbola xy = 8. As it reaches the point (4, 2), the y-coordinate is decreasing at a rate of 3 cm/s. How fast is the x-coordinate of the point changing at that instant?
Answer Preview: dx dt 6 Thus the x coordinat…
, Chapter: 1 -Problem: 15 >> Make a rough sketch of the graph of the function. Do not use a calculator. Just use the graphs given in Figures 3 and 13 and, if necessary, the transformations of Section 1.3.y = 1 €“ 1/2 „¯€“x Figure 3: Figure 13: Transcribed Image Text: yA 10* (45 4* 2* 1.5* ? y. (1, 1) (1, 1) ? ? (a) f(x)= x %
Answer Preview: We start with the graph of y x Figure 16 and reflect about the y axis to …
, Chapter: 10 -Problem: 5 >> Find an equation of the tangent to the curve at the point corresponding to the given value of the parameter. Transcribed Image Text: x = t cos t, y = t sin t; t =
Answer Preview: x tcost y tsint t dy dt t cost sint dx dt d…
, Chapter: 4 -Problem: 17 >> Sketch the graph of a function that satisfies the given conditions. 0 for 0 < x < 3, f"(x) < 0 for x > 3, f'(x) < 0 for 0 < x < 2, lim f(x) = -2 " style="" class="fr-fic fr-dib"> Transcribed Image Text: f is odd, , f'(x) > 0 for x> 2, f"(x) > 0 for 0 < x < 3, f"(x) < 0 for x > 3, f'(x) < 0 for 0 < x
Answer Preview: f is odd f…
, Chapter: 12 -Problem: 2 >> Let B be a solid box with length L, width W, and height H. Let S be the set of all points that are a distance at most 1 from some point of B. Express the volume of S in terms of L, W, and H.
Answer Preview: Try an analogous problem in two dimensions Consider a rectangle with le…
, Chapter: 15 -Problem: 14 >> Express D as a region of type I and also as a region of type II. Then evaluate the double integral in two ways. Transcribed Image Text: xy dA, Dis enclosed by the curves y = x², y = 3x
Answer Preview: y 3x or x y 3 D 3 9 y x or x X The curves y x and …
, Chapter: 3 -Problem: 11 >> Differentiate.f(?) = sin (?)/1 + cos (?)
Answer Preview: f 0 0 sin 0 1 cos 0 …
, Chapter: 3 -Problem: 15 >> Differentiate.f (?) = ? cos ? sin ?
Answer Preview: Using Exercise 3 2 61 a f cos sin …
, Chapter: 16 -Problem: 3 >> Determine whether or not F is a conservative vector field. If it is, find a function f such that F = ?f.F(x, y) = (xy + y2) i + (x2 + 2xy) j
Answer Preview: Let P x y xy y and Q x y …
, Chapter: 11 -Problem: 37 >> The meaning of the decimal representation of a number 0.d1d2d3 . . . (where the digit di is one of the numbers 0, 1, 2, . . . , 9) is that Transcribed Image Text: di d2 0.d, d2dzd4 ... dz d4 10 102 103 104
Answer Preview: 9 10 10 will always converg…
, Chapter: 14 -Problem: 2 >> What is a function of three variables? How can you visualize such a function?
Answer Preview: A function will basically tells about a relationship between an independent variable and dependent v…
, Chapter: 14 -Problem: 17 >> Find the first partial derivatives.S(u, v, w) = u arctan(v?w)
Answer Preview: G x y z ez sin y z Gz z…
, Chapter: 16 -Problem: 47 >> Find the area of the surface.The part of the paraboloid y = x2 + z2 that lies within the cylinder x2 + z2 = 16
Answer Preview: A parametric representation of the surface is x x y …
, Chapter: 7 -Problem: 84 >> We know that is a continuous function by FTC1, though it is not an elementary function. The functionsare not elementary either, but they can be expressed in terms of F. Evaluate the following integrals in terms of F.(a)(b) Transcribed Image Text: F(x) = f, e" dt eer
Answer Preview: a b Another method Subs…
, Chapter: 3 -Problem: 56 >> For what value of x does the graph of f (x) = ex - 2x have a horizontal tangent?
Answer Preview: so f has a hori…
, Chapter: 8 -Problem: 109 >> In the following exercises, two sequences are given, one of which initially has smaller values, but eventually “overtakes” the other sequence. Find the sequence with the larger growth rate and the value of n at which it overtakes the other sequence.an = n! and bn = n0.7n, n ? 2
Answer Preview: Experiment with a few widely separated values of n: n 1 10 100 1000 n! 1 3 63 x 106 9 33 x …
, Chapter: 15 -Problem: 11 >> Evaluate the double integral by first identifying it as the volume of a solid. Transcribed Image Text: Sle (4 – 2y) dA, R= [0, 1] × [0, 1]
Answer Preview: z 4 2y 0 for 0 y 1 so we can interpret the integral as th…
, Chapter: 14 -Problem: 86 >> Cobb and Douglas used the equation P(L, K) = .01L0.75K0.25 to model the American economy from 1899 to 1922, where L is the amount of labor and K is the amount of capital. (See Example 14.1.3.) (a) Calculate PL and PK. (b) Find the marginal productivity of labor and the marginal productivity of capital in the year 1920, when L = 194 and K = 407 (compared with the assigned values L = 100 and K = 100
Answer Preview: a P L K 1 01Z0 75 0 25 Px L K 1 01L0 75 0 25K 0 75 0 252510 75 K 0 75 PL L K 1 01 0 75L …
, Chapter: 15 -Problem: 50 >> If E is the solid of Exercise 18 with density function p(x, y, z) = x2 + y2, find the following quantities, correct to three decimal places. (a) The mass (b) The center of mass (c) The moment of inertia about the z-axis
Answer Preview: 3 a m S S S 9 y2 x y dz dy dx 56 11 2 b …
, Chapter: 11 -Problem: 37 >> Test the series for convergence or divergence. Transcribed Image Text: ? (y-1)" n=1
Answer Preview: lim an lim 2 1 1 …
, Chapter: 7 -Problem: 12 >> Evaluate the integral. Transcribed Image Text: 1/2 " (2 – sin0)² de 7/2
Answer Preview: 2 f 2 sin 0 d0 S 4 4 s…
, Chapter: 3 -Problem: 20 >> Calculate y'.y = ex sec x
Answer Preview: sec x y es x sec …
,
Additional Information
Book:
Calculus Early Transcendentals
Isbn:
ISBN: 978-1285741550
Edition:
8th edition
Author:
Authors: James Stewart
Image:
1779.jpg
7 Reviews for Calculus Early Transcendentals Textbook Questions And Answers
Gerardo Espinoza
Devyn Palmer
One stop shopping for the best homework advice you can get. Tried and proven time after time.
8 1 Reply
Cora Price
8 2 Reply
Roland Cowan
11 0 Reply
Anabelle Griffith
9 1 Reply
12
