 15.1: A contour map is shown for a function f on the square R f0, 3g 3 f0...
 15.2: Use the Midpoint Rule to estimate the integral in Exercise 1.
 15.3: Calculate the iterated integral.
 15.4: Calculate the iterated integral.
 15.5: Calculate the iterated integral.
 15.6: Calculate the iterated integral.
 15.7: Calculate the iterated integral.
 15.8: Calculate the iterated integral.
 15.9: Write yyR fsx, yd dA as an iterated integral, where R is the region...
 15.10: Write yyR fsx, yd dA as an iterated integral, where R is the region...
 15.11: The cylindrical coordinates of a point are (2s3 , y3, 2). Find the ...
 15.12: The rectangular coordinates of a point are s2, 2, 21d. Find the cyl...
 15.13: The spherical coordinates of a point are s8, y4, y6d. Find the rect...
 15.14: Identify the surfaces whose equations are given. (a) y4 (b) y4
 15.15: Write the equation in cylindrical coordinates and in spherical coor...
 15.16: Sketch the solid consisting of all points with spherical coordinate...
 15.17: Describe the region whose area is given by the integral y y2 0 y si...
 15.18: Describe the solid whose volume is given by the integral y y2 0 y y...
 15.19: Calculate the iterated integral by first reversing the order of int...
 15.20: Calculate the iterated integral by first reversing the order of int...
 15.21: Calculate the value of the multiple integral
 15.22: Calculate the value of the multiple integral
 15.23: Calculate the value of the multiple integral
 15.24: Calculate the value of the multiple integral
 15.25: Calculate the value of the multiple integral
 15.26: Calculate the value of the multiple integral
 15.27: Calculate the value of the multiple integral
 15.28: Calculate the value of the multiple integral
 15.29: Calculate the value of the multiple integral
 15.30: Calculate the value of the multiple integral
 15.31: Calculate the value of the multiple integral
 15.32: Calculate the value of the multiple integral
 15.33: Calculate the value of the multiple integral
 15.34: Calculate the value of the multiple integral
 15.35: Find the volume of the given solid.
 15.36: Find the volume of the given solid.
 15.37: Find the volume of the given solid.
 15.38: Find the volume of the given solid.
 15.39: Find the volume of the given solid.
 15.40: Find the volume of the given solid.
 15.41: Consider a lamina that occupies the region D bounded by the parabol...
 15.42: A lamina occupies the part of the disk x 2 1 y 2 < a 2 that lies in...
 15.43: (a) Find the centroid of a solid right circular cone with height h ...
 15.44: Find the area of the part of the cone z 2 a 2 sx 2 1 y 2 d between ...
 15.45: Find the area of the part of the surface z x 2 1 y that lies above ...
 15.46: Graph the surface z x sin y, 23 < x < 3, 2 < y < , and nd its surfa...
 15.47: Use polar coordinates to evaluate y 3 0 y s92x 2 2s92x 2 sx 3 1 xy ...
 15.48: Use spherical coordinates to evaluate y 2 22 y s42y 2 0 y s42x22y2 ...
 15.49: If D is the region bounded by the curves y 1 2 x 2 and y e x , nd t...
 15.50: Find the center of mass of the solid tetrahedron with vertices s0, ...
 15.51: The joint density function for random variables X and Y is fsx, yd ...
 15.52: A lamp has three bulbs, each of a type with average lifetime 800 ho...
 15.53: Rewrite the integral y 1 21 y 1 x 2 y 12y 0 fsx, y, zd dz dy dx as ...
 15.54: Give ve other iterated integrals that are equal to y 2 0 y y 3 0 y ...
 15.55: Use the transformation u x 2 y, v x 1 y to evaluate yy R x 2 y x 1 ...
 15.56: Use the transformation x u 2 , y v 2 , z w 2 to nd the volume of th...
 15.57: Use the change of variables formula and an appropriate transformati...
 15.58: The Mean Value Theorem for double integrals says that if f is a con...
 15.59: Suppose that f is continuous on a disk that contains the point sa, ...
 15.60: (a) Evaluate y D y 1 sx 2 1 y 2 d ny2 dA, where n is an integer and...
Solutions for Chapter 15: Calculus: Early Transcendentals 8th Edition
Full solutions for Calculus: Early Transcendentals  8th Edition
ISBN: 9781285741550
Solutions for Chapter 15
Get Full SolutionsThis textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 8. Since 60 problems in chapter 15 have been answered, more than 7963 students have viewed full stepbystep solutions from this chapter. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9781285741550. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 15 includes 60 full stepbystep solutions.

Acute angle
An angle whose measure is between 0° and 90°

Annual percentage rate (APR)
The annual interest rate

Constraints
See Linear programming problem.

Cosine
The function y = cos x

DMS measure
The measure of an angle in degrees, minutes, and seconds

Horizontal line
y = b.

Inverse properties
a + 1a2 = 0, a # 1a

Irreducible quadratic over the reals
A quadratic polynomial with real coefficients that cannot be factored using real coefficients.

Limit
limx:aƒ1x2 = L means that ƒ(x) gets arbitrarily close to L as x gets arbitrarily close (but not equal) to a

Maximum rvalue
The value of r at the point on the graph of a polar equation that has the maximum distance from the pole

Multiplicative identity for matrices
See Identity matrix

Period
See Periodic function.

Polar distance formula
The distance between the points with polar coordinates (r1, ?1 ) and (r2, ?2 ) = 2r 12 + r 22  2r1r2 cos 1?1  ?22

Polar form of a complex number
See Trigonometric form of a complex number.

Range (in statistics)
The difference between the greatest and least values in a data set.

Range of a function
The set of all output values corresponding to elements in the domain.

Richter scale
A logarithmic scale used in measuring the intensity of an earthquake.

Right circular cone
The surface created when a line is rotated about a second line that intersects but is not perpendicular to the first line.

Secant
The function y = sec x.

Work
The product of a force applied to an object over a given distance W = ƒFƒ ƒAB!ƒ.