 13.3.1: Draw the region 51r, u2: 1 r 2, 0 u p>26. Why is it called a polar ...
 13.3.2: Write the double integral 4R f 1x, y2 dA as an iterated integral in...
 13.3.3: Sketch the region of integration for the integral L p>6 p>6 L cos ...
 13.3.4: Explain why the element of area in Cartesian coordinates dx dy beco...
 13.3.5: How do you find the area of a region R = 51r, u2: 0 g1u2 r h1u2, a ...
 13.3.6: How do you find the average value of a function over a region that ...
 13.3.7: 710. Polar rectangles Sketch the following polar rectangles. R = 51...
 13.3.8: 710. Polar rectangles Sketch the following polar rectangles. R = 51...
 13.3.9: 710. Polar rectangles Sketch the following polar rectangles. R = 51...
 13.3.10: 710. Polar rectangles Sketch the following polar rectangles. R = 51...
 13.3.11: 1114. Solids bounded by paraboloids Find the volume of the solid be...
 13.3.12: 1114. Solids bounded by paraboloids Find the volume of the solid be...
 13.3.13: 1114. Solids bounded by paraboloids Find the volume of the solid be...
 13.3.14: 1114. Solids bounded by paraboloids Find the volume of the solid be...
 13.3.15: 1518. Solids bounded by hyperboloids Find the volume of the solid b...
 13.3.16: 1518. Solids bounded by hyperboloids Find the volume of the solid b...
 13.3.17: 1518. Solids bounded by hyperboloids Find the volume of the solid b...
 13.3.18: 1518. Solids bounded by hyperboloids Find the volume of the solid b...
 13.3.19: 1922. Volume between surfaces Find the volume of the following soli...
 13.3.20: 1922. Volume between surfaces Find the volume of the following soli...
 13.3.21: 1922. Volume between surfaces Find the volume of the following soli...
 13.3.22: 1922. Volume between surfaces Find the volume of the following soli...
 13.3.23: 2328. Cartesian to polar coordinates Sketch the given region of int...
 13.3.24: 2328. Cartesian to polar coordinates Sketch the given region of int...
 13.3.25: 2328. Cartesian to polar coordinates Sketch the given region of int...
 13.3.26: 2328. Cartesian to polar coordinates Sketch the given region of int...
 13.3.27: 2328. Cartesian to polar coordinates Sketch the given region of int...
 13.3.28: 2328. Cartesian to polar coordinates Sketch the given region of int...
 13.3.29: 2932. Island problems The surface of an island is defined by the fo...
 13.3.30: 2932. Island problems The surface of an island is defined by the fo...
 13.3.31: 2932. Island problems The surface of an island is defined by the fo...
 13.3.32: 2932. Island problems The surface of an island is defined by the fo...
 13.3.33: 3338. Describing general regions Sketch the following regions R. Th...
 13.3.34: 3338. Describing general regions Sketch the following regions R. Th...
 13.3.35: 3338. Describing general regions Sketch the following regions R. Th...
 13.3.36: 3338. Describing general regions Sketch the following regions R. Th...
 13.3.37: 3338. Describing general regions Sketch the following regions R. Th...
 13.3.38: 3338. Describing general regions Sketch the following regions R. Th...
 13.3.39: 3944. Computing areas Sketch each region and use a double integral ...
 13.3.40: 3944. Computing areas Sketch each region and use a double integral ...
 13.3.41: 3944. Computing areas Sketch each region and use a double integral ...
 13.3.42: 3944. Computing areas Sketch each region and use a double integral ...
 13.3.43: 3944. Computing areas Sketch each region and use a double integral ...
 13.3.44: 3944. Computing areas Sketch each region and use a double integral ...
 13.3.45: 4548. Average values Find the following average values. The average...
 13.3.46: 4548. Average values Find the following average values. The average...
 13.3.47: 4548. Average values Find the following average values. The average...
 13.3.48: 4548. Average values Find the following average values. The average...
 13.3.49: Explain why or why not Determine whether the following statements a...
 13.3.50: 5057. Miscellaneous integrals Evaluate the following integrals usin...
 13.3.51: 5057. Miscellaneous integrals Evaluate the following integrals usin...
 13.3.52: 5057. Miscellaneous integrals Evaluate the following integrals usin...
 13.3.53: 5057. Miscellaneous integrals Evaluate the following integrals usin...
 13.3.54: 5057. Miscellaneous integrals Evaluate the following integrals usin...
 13.3.55: 5057. Miscellaneous integrals Evaluate the following integrals usin...
 13.3.56: 5057. Miscellaneous integrals Evaluate the following integrals usin...
 13.3.57: 5057. Miscellaneous integrals Evaluate the following integrals usin...
 13.3.58: Areas of circles Use integration to show that the circles r = 2a co...
 13.3.59: Filling bowls with water Which bowl holds more water if it is fille...
 13.3.60: Equal volumes To what height (above the bottom of the bowl) must th...
 13.3.61: Volume of a hyperbolic paraboloid Consider the surface z = x2  y2....
 13.3.62: Slicing a hemispherical cake A cake is shaped like a hemisphere of ...
 13.3.63: 6366. Improper integrals Improper integrals arise in polar coordina...
 13.3.64: 6366. Improper integrals Improper integrals arise in polar coordina...
 13.3.65: 6366. Improper integrals Improper integrals arise in polar coordina...
 13.3.66: 6366. Improper integrals Improper integrals arise in polar coordina...
 13.3.67: Limaon loops The limaon r = b + a cos u has an inner loop if b 6 a ...
 13.3.68: Mass from density data The following table gives the density (in un...
 13.3.69: A mass calculation Suppose the density of a thin plate represented ...
 13.3.70: Area formula In Section 10.3 it was shown that the area of a region...
 13.3.71: Normal distribution An important integral in statistics associated ...
 13.3.72: Existence of integrals For what values of p does the integral OR dA...
 13.3.73: Integrals in strips Consider the integral I = OR dA 11 + x2 + y2 22...
 13.3.74: Area of an ellipse In polar coordinates an equation of an ellipse w...
Solutions for Chapter 13.3: Calculus: Early Transcendentals 2nd Edition
Full solutions for Calculus: Early Transcendentals  2nd Edition
ISBN: 9780321947345
Solutions for Chapter 13.3
Get Full SolutionsSince 74 problems in chapter 13.3 have been answered, more than 57520 students have viewed full stepbystep solutions from this chapter. Chapter 13.3 includes 74 full stepbystep solutions. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321947345. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 2. This expansive textbook survival guide covers the following chapters and their solutions.

Acute triangle
A triangle in which all angles measure less than 90°

Continuous function
A function that is continuous on its entire domain

Double inequality
A statement that describes a bounded interval, such as 3 ? x < 5

equation of a parabola
(x  h)2 = 4p(y  k) or (y  k)2 = 4p(x  h)

equation of an ellipse
(x  h2) a2 + (y  k)2 b2 = 1 or (y  k)2 a2 + (x  h)2 b2 = 1

Halfangle identity
Identity involving a trigonometric function of u/2.

Initial point
See Arrow.

Intermediate Value Theorem
If ƒ is a polynomial function and a < b , then ƒ assumes every value between ƒ(a) and ƒ(b).

Inverse cosine function
The function y = cos1 x

Inverse function
The inverse relation of a onetoone function.

Lefthand limit of f at x a
The limit of ƒ as x approaches a from the left.

Linear inequality in x
An inequality that can be written in the form ax + b < 0 ,ax + b … 0 , ax + b > 0, or ax + b Ú 0, where a and b are real numbers and a Z 0

Numerical derivative of ƒ at a
NDER f(a) = ƒ1a + 0.0012  ƒ1a  0.00120.002

Parametrization
A set of parametric equations for a curve.

Polar equation
An equation in r and ?.

Radius
The distance from a point on a circle (or a sphere) to the center of the circle (or the sphere).

Remainder polynomial
See Division algorithm for polynomials.

Term of a polynomial (function)
An expression of the form anxn in a polynomial (function).

zaxis
Usually the third dimension in Cartesian space.

Zero matrix
A matrix consisting entirely of zeros.