 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 6420 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.

Average rate of change of ƒ over [a, b]
The number ƒ(b)  ƒ(a) b  a, provided a ? b.

Conic section (or conic)
A curve obtained by intersecting a doublenapped right circular cone with a plane

Dependent event
An event whose probability depends on another event already occurring

Derivative of ƒ
The function defined by ƒ'(x) = limh:0ƒ(x + h)  ƒ(x)h for all of x where the limit exists

Direction vector for a line
A vector in the direction of a line in threedimensional space

Division algorithm for polynomials
Given ƒ(x), d(x) ? 0 there are unique polynomials q1x (quotient) and r1x(remainder) ƒ1x2 = d1x2q1x2 + r1x2 with with either r1x2 = 0 or degree of r(x) 6 degree of d1x2

Exponent
See nth power of a.

Exponential regression
A procedure for fitting an exponential function to a set of data.

Finite series
Sum of a finite number of terms.

Head minus tail (HMT) rule
An arrow with initial point (x1, y1 ) and terminal point (x2, y2) represents the vector <8x 2  x 1, y2  y19>

Horizontal shrink or stretch
See Shrink, stretch.

Inductive step
See Mathematical induction.

Limit at infinity
limx: qƒ1x2 = L means that ƒ1x2 gets arbitrarily close to L as x gets arbitrarily large; lim x: q ƒ1x2 means that gets arbitrarily close to L as gets arbitrarily large

Linear equation in x
An equation that can be written in the form ax + b = 0, where a and b are real numbers and a Z 0

Local maximum
A value ƒ(c) is a local maximum of ƒ if there is an open interval I containing c such that ƒ(x) < ƒ(c) for all values of x in I

Multiplication property of inequality
If u < v and c > 0, then uc < vc. If u < and c < 0, then uc > vc

Remainder polynomial
See Division algorithm for polynomials.

Simple harmonic motion
Motion described by d = a sin wt or d = a cos wt

Vertical line
x = a.

Xmin
The xvalue of the left side of the viewing window,.