Calculus and Its Applications Plus MyLab Math with Pearson eText -- Access Card Package (11th Edition) (Bittinger, Ellenbogen & Surgent, The Calculus and Its Applications Series)
11th Edition
ISBN: 9780133795561
Author: Marvin L. Bittinger, David J. Ellenbogen, Scott J. Surgent
Publisher: PEARSON
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Chapter CR, Problem 2E
To determine
To calculate: The slope and the y-intercept of the given equation
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(12 points) Let
E={(x, y, z)|x²+ y² + z² ≤ 4, x, y, z > 0}.
(a) (4 points) Describe the region E using spherical coordinates, that is, find p, 0, and such
that
(x, y, z) (psin cos 0, psin sin 0, p cos) € E.
(b) (8 points) Calculate the integral
E
xyz dV using spherical coordinates.
(10 points) Let f(x, y, z) = ze²²+y². Let
E = {(x, y, z) | x² + y² ≤ 4,2 ≤ z < 3}.
Calculate the integral
y,
f(x, y, z) dV.
(14 points) Let f: R3 R and T: R3.
→R³ be defined by
f(x, y, z) = ln(x²+ y²+2²),
T(p, 0,4)=(psin cos 0, psin sin, pcos).
(a) (4 points) Write out the composition g(p, 0, 4) = (foT)(p,, ) explicitly. Then calculate the
gradient Vg directly, i.e. without using the chain rule.
(b) (4 points) Calculate the gradient Vf(x, y, z) where (x, y, z) = T(p, 0,4).
(c) (6 points) Calculate the derivative matrix DT(p, 0, p). Then use the Chain Rule to calculate
Vg(r,0,4).
Chapter CR Solutions
Calculus and Its Applications Plus MyLab Math with Pearson eText -- Access Card Package (11th Edition) (Bittinger, Ellenbogen & Surgent, The Calculus and Its Applications Series)
Ch. CR - Write an equation of the line with slope 4 and...Ch. CR - Prob. 2ECh. CR - For f(x)=x25, find f(x+h). x2+2xh+h25Ch. CR - 4. a. Graph:
b. Find.
c. Find.
d. Is f...Ch. CR - Prob. 5ECh. CR - Find each limit, if it exists. If a limit does not...Ch. CR - Find each limit, if it exists. If a limit does not...Ch. CR - Find each limit, if it exists. If a limit does not...Ch. CR - Find each limit, if it exists. If a limit does not...Ch. CR - Find each limit, if it exists. If a limit does not...
Ch. CR - Find each limit, if it exists. If a limit does not...Ch. CR - For Exercises 12-14, refer to the following graph...Ch. CR - For Exercises 12-14, refer to the following graph...Ch. CR - For Exercises 12-14, refer to the following graph...Ch. CR - Differentiate. y=9x+3Ch. CR - Differentiate. y=x27x+3Ch. CR - Differentiate. y=x1/4Ch. CR - Differentiate. f(x)=x6Ch. CR - Prob. 19ECh. CR - Differentiate.
22.
Ch. CR - Prob. 21ECh. CR - Differentiate. y=elnxCh. CR - Prob. 23ECh. CR - Differentiate.
24.
Ch. CR - Differentiate.
25.
Ch. CR - 26. For find.
Ch. CR - Business: average cost. Doubletake Clothing finds...Ch. CR -
28. Differentiate implicitly to find if .
Ch. CR - Find an equation of the tangent line to the graph...Ch. CR - 30. Find the x-value(s) at which the tangent line...Ch. CR - Sketch the graph of each function. List the label...Ch. CR - Prob. 32ECh. CR - Sketch the graph of each function. List the label...Ch. CR - Prob. 34ECh. CR - Find the absolute maximum and minimum values, if...Ch. CR - Prob. 36ECh. CR - Prob. 37ECh. CR - Prob. 38ECh. CR - 39. Business: minimizing inventory costs. An...Ch. CR - Prob. 40ECh. CR - Business: exponential growth. Friedas Frozen...Ch. CR - Prob. 42ECh. CR - 43. Business: approximating cost average. A square...Ch. CR - Prob. 44ECh. CR - Prob. 46ECh. CR - Prob. 47ECh. CR - Evaluate.
48. (Use Table 1 on pp. 431-432)
Ch. CR - Prob. 49ECh. CR - Evaluate. (x+3)lnxdxCh. CR - Prob. 51ECh. CR - Prob. 52ECh. CR - 53. Find the area under the graph of over the...Ch. CR - Business: present value. Find the present value of...Ch. CR - Prob. 55ECh. CR - Evaluate.
56. Business: contract buyout. An...Ch. CR - Prob. 57ECh. CR - 58. Economic: supply and demand. Demand and supply...Ch. CR - 59. Find the volume of the solid of revolution...Ch. CR - 60. Find the volume of the solid of revolution...Ch. CR - Consider the data in the following table. Age of...Ch. CR - Prob. 62ECh. CR - Given find each of the following.
63.
Ch. CR - Prob. 64ECh. CR - 65. Maximize subject to the constraint.
Ch. CR - 66. Evaluate
.
Ch. CR - Prob. 67ECh. CR - Solve the differential equation dy/dx=xy.Ch. CR - Solve the differential equation y+4xy=3x, where...Ch. CR - Prob. 70ECh. CR - Prob. 71ECh. CR - Business: distribution of weights. The weight, in...Ch. CR - Business: wait times. The wait time t in minutes,...Ch. CR - Prob. 74ECh. CR - 75. Business: distribution of salaries. The...
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