 13.1: In 1 through 5, evaluate the given integral by first revirsing the ...
 13.2: In 1 through 5, evaluate the given integral by first revirsing the ...
 13.3: In 1 through 5, evaluate the given integral by first revirsing the ...
 13.4: In 1 through 5, evaluate the given integral by first revirsing the ...
 13.5: In 1 through 5, evaluate the given integral by first revirsing the ...
 13.6: The double integral I I  r/r',/.r' J,, J. \ is an improper integra...
 13.7: Find the volume of the soiid f that lies below the paraboloid : : ,...
 13.8: Find by integration in cylindrical coordinates the volume bounded b...
 13.9: Use integration in spherical coordinates to find the volume and cen...
 13.10: Find the volunre of the solid bounded by the elliptic paraboloids :...
 13.11: Find the volume bounded by the paraboloid l = .tr + 3:r and the par...
 13.12: Find the volume of the region bounded by the parabolic cylinders: =...
 13.13: Find the volume of the region bounded by the elliptical cylinder r ...
 13.14: Show that the volume of the solid bounded by the elliptical cylinde...
 13.15: Lel R be the firstquadrant region bounded by the curve .rr + rlt :...
 13.16: The region bounded by l = .rr and r = r'r: 6(r.r') : ..: + .r'l
 13.17: The region bounded by,r : 2,r'r and r': : r  4: 6(.r. r') = j
 13.18: The region between r' = lnr and the,taxis over the interval llr !...
 13.19: The circle bounded bv r' : 2 cos d: 6 (r'. 0) = ,t (3 senstanll
 13.20: The legion of 19: d(r. 0) : r
 13.21: , Use the iirst theorem of Pappus to lind the r,coordinate of rhe ...
 13.22: (a) Use the nrst theorem of Pappus to find the centroid of the firs...
 13.23: Find the centroid of the region in the 5plane bounded by the .rax...
 13.24: Find the volume of the solid that lies below the paraboiic cylinder...
 13.25: Use cylindrical coordinates to Rnd the volume of the icecream cone ...
 13.26: . Find the volume and centrcid of the icecream cone bounded above ...
 13.27: A homogeneous solid circular cone has mass M and base radius a. Fin...
 13.28: Find the mass of the iirst octant of the ball p ! a if its densily ...
 13.29: Find the moment of inenia around the raxis of the homogeneous soli...
 13.30: Find the volume of the region in the first octant rhar is bounded b...
 13.31: Find the moment of inenia around the axis of the homogeneous regi...
 13.32: Find the volume of the solid obtained by revolving around the )axi...
 13.33: Find the volume of the solid obtained by revolving around the .jra...
 13.34: Find the volume of the solid torus obtained by revolving the disk 0...
 13.35: Assume that the to.us of has uniform density 6. Find its moment of ...
 13.36: Show thal the average distance o[ the pninrs ota disk of radiu\ d f...
 13.37: Show that the average distance of the points of a disk of radius (l...
 13.38: A circle of radius I is interior to and tangent to a circle of radi...
 13.39: Show that the average distance of the points of a spherical ball of...
 13.40: Show that the average distance of the points of a spherical ball of...
 13.41: A sphere of radius I is interior to and tangent to a sphere of radi...
 13.42: A right circular cone has radius R and height 11. Find the average ...
 13.43: A right circular cone has radius R and height 11. Find the average ...
 13.44: Find the surface area of the pan of the sudace a = J'r  r: that is...
 13.45: Let A be the suface area of the zone on the sphere p : d between th...
 13.46: Find the surface area of the pan of the sphere p = 2 that is inside...
 13.47: A square hole \\'ith side length 2 is cut through a cone of height ...
 13.48: Numerical)y approximate the surface area ol the part of the parabol...
 13.49: A "fence" of Variable height h0) stands above the plane curve (r (t...
 13.50: Apply the formula of .19 to compute rhe area of the pan ofthe cylin...
 13.51: Find the polar moment of inertia ol the lirstquadrant region ol co...
 13.52: Substitute rr :.\  1, and r) :.r + ] to evaluate ll /r'1\ / / ex...
 13.53: Use el)ipsoidal coordinates .r  .tpsindcos0. 1. = bp sin @ sin e....
 13.54: . Let R be the firsGquadrant rcgion bounded by the lemniscates 12 :...
 13.55: A 2by2 square hole is cur symmelrically rhrough a sphere of radiu...
 13.56: Show that the volume enclosed by the surface r1l3 + ),2/3 +,1/3 _ a...
 13.57: Show that the volume enclosed by the surface lrlr 3 + lll' J + lrlr...
 13.58: Find the average of the squarc of the distance of points of rhe sol...
 13.59: A cube C of edge length 1 is rotated around a line passing through ...
Solutions for Chapter 13: Calculus:Early Transcendentals 7th Edition
Full solutions for Calculus:Early Transcendentals  7th Edition
ISBN: 9780131569898
Solutions for Chapter 13
Get Full SolutionsCalculus:Early Transcendentals was written by and is associated to the ISBN: 9780131569898. Chapter 13 includes 59 full stepbystep solutions. Since 59 problems in chapter 13 have been answered, more than 10013 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Calculus:Early Transcendentals, edition: 7.

Bounded above
A function is bounded above if there is a number B such that ƒ(x) ? B for all x in the domain of ƒ.

Compound interest
Interest that becomes part of the investment

Direct variation
See Power function.

Directed line segment
See Arrow.

Distance (in Cartesian space)
The distance d(P, Q) between and P(x, y, z) and Q(x, y, z) or d(P, Q) ((x )  x 2)2 + (y1  y2)2 + (z 1  z 2)2

Equally likely outcomes
Outcomes of an experiment that have the same probability of occurring.

Graph of a polar equation
The set of all points in the polar coordinate system corresponding to the ordered pairs (r,?) that are solutions of the polar equation.

Horizontal Line Test
A test for determining whether the inverse of a relation is a function.

Inverse variation
See Power function.

Main diagonal
The diagonal from the top left to the bottom right of a square matrix

Negative angle
Angle generated by clockwise rotation.

nth root
See Principal nth root

Onetoone function
A function in which each element of the range corresponds to exactly one element in the domain

Perpendicular lines
Two lines that are at right angles to each other

Rational numbers
Numbers that can be written as a/b, where a and b are integers, and b ? 0.

Sequence
See Finite sequence, Infinite sequence.

Solve graphically
Use a graphical method, including use of a hand sketch or use of a grapher. When appropriate, the approximate solution should be confirmed algebraically

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.