 6.1: t:t1 t2: a=0.b:3
 6.2: r:l,t4. a=1,b=1
 6.3: r':." sin lrtlr  lt: n  0. i': l
 6.4: In 4 through 8, a solid ettends alortg tlte rais ft'otn r : a to r...
 6.5: In 4 through 8, a solid ettends alortg tlte rais ft'otn r : a to r...
 6.6: In 4 through 8, a solid ettends alortg tlte rais ft'otn r : a to r...
 6.7: In 4 through 8, a solid ettends alortg tlte rais ft'otn r : a to r...
 6.8: In 4 through 8, a solid ettends alortg tlte rais ft'otn r : a to r...
 6.9: Suppose that rainfall begins at time r = 0 and that the rate after ...
 6.10: The base of a cenain solid is the region in the first quadrant boun...
 6.11: Find the volume of the solid generated by revolving around the ra...
 6.12: Find the volume of the solid genrated by revolving the region bound...
 6.13: A wire made ofcopper (density 8.5 g/cmr) is shaped like a helix tha...
 6.14: Derive the formula V = Fh(ri + rrrr + r,:) for the volume of a frus...
 6.15: Suppose that the point P lies on a line perpendicular to the lrpl...
 6.16: Figure 6.MP1 shows the region R bounded by the ellipse (rlaf + (!lb...
 6.17: Figure 6.MP2 shows the region R bounded by rhe hyperbola (r/a)r  (...
 6.18: VLrr .'{   l: tne.\xxi\
 6.19: V(r) : rt(1 + 3r),  161; the raxis
 6.20: V(t) ;z[(l + 3/r)r,] 8l: the r.axis
 6.21: Use the integral formula to find the volume of the solid generated ...
 6.22: Use the nethod of cylindlical shells to lind the volume of the soli...
 6.23: Find the length of thecurver': +.r1,: rr': from,r: I
 6.24: Find the area of the surface generated by revoiving the curve of ar...
 6.25: Find the lengrh of the curve:t = j{_rair2_r,2/l)from): I tot=8.
 6.26: Find the area of the surface generated by revoh'ing the curve of ar...
 6.27: Find the area of the surface genelated by revolving the curve of ar...
 6.28: If r S a < b = r. then a "spherical zone" of "height" h : b a is g...
 6.29: Apply the result of to show that the surface area of a sphere of ra...
 6.30: Let R denote the region bounded by the curves l : 2rl and t.r : ,lr...
 6.31: Find the natural length I of a spring il {ive times as much $ork is...
 6.32: A steel beam weighing 1000 ]b hangs from a 50ft cable that weighs ...
 6.33: A spherical tank of radius R (in fee, is inirially lull of oil of d...
 6.34: Horv much work is done by a colony of ants in building a conical an...
 6.35: The gravitational attraction below the earth's surface is directly ...
 6.36: How much work is done in digging the hole of Probiem 35that is. in...
 6.37: Suppose that a dam is shaped like a trapezoid of height 100 ft. 300...
 6.38: Suppose that a dam has the same top and bottom lengths as the dam o...
 6.39: For c > 0. the graphs of r. : clrl and _r. : c bound a plane region...
 6.40: Find the centroids of the curves in 40 through 43.
 6.41: Find the centroids of the curves in 40 through 43.
 6.42: Find the centroids of the curves in 40 through 43.
 6.43: Find the centroids of the curves in 40 through 43.
 6.44: Find the centrcid of the plane region in the 6rst quadrant that is ...
 6.45: . Find the centroid ofthe plane region bounded by the curves r = 2...
 6.46: Let T be the plan triangle with venices (0. 0). (a. b ). and (c, 0)...
 6.47: Use the nrst theorem of Pappus to find the rcoordinate of the cent...
 6.48: (a) Use the first theorem of Pappus to find the centroid of the fir...
 6.49: 9. Let T be the triangle in the first quadrant with one vertex at (...
 6.50: Suppose that r is an even positive inteser. Ler J be an nsided re...
 6.51: Suppose that,? is a positive integer, Let R,, denote the region bou...
 6.52: Let the region R be the Llnion of the semicircular disk .\': + \':5...
 6.53: Evaluate the indefinite integrals in 53 through 64.
 6.54: Evaluate the indefinite integrals in 53 through 64.
 6.55: Evaluate the indefinite integrals in 53 through 64.
 6.56: Evaluate the indefinite integrals in 53 through 64.
 6.57: Evaluate the indefinite integrals in 53 through 64.
 6.58: Evaluate the indefinite integrals in 53 through 64.
 6.59: Evaluate the indefinite integrals in 53 through 64.
 6.60: Evaluate the indefinite integrals in 53 through 64.
 6.61: Evaluate the indefinite integrals in 53 through 64.
 6.62: Evaluate the indefinite integrals in 53 through 64.
 6.63: Evaluate the indefinite integrals in 53 through 64.
 6.64: Evaluate the indefinite integrals in 53 through 64.
 6.65: A grain warehouse holds B bushels of gmin, which is deteriorating i...
 6.66: You have bonowed $1000 at 107. annual interest. compounded continuo...
 6.67: Blood samples from 1000 students are to be tested for a certain dis...
 6.68: Find the length of the curve r' : lxr  j ln,t from .r = I
 6.69: Dffirentiate the functions in 69 through 88.
 6.70: Dffirentiate the functions in 69 through 88.
 6.71: Dffirentiate the functions in 69 through 88.
 6.72: Dffirentiate the functions in 69 through 88.
 6.73: Dffirentiate the functions in 69 through 88.
 6.74: Dffirentiate the functions in 69 through 88.
 6.75: Dffirentiate the functions in 69 through 88.
 6.76: Dffirentiate the functions in 69 through 88.
 6.77: Dffirentiate the functions in 69 through 88.
 6.78: Dffirentiate the functions in 69 through 88.
 6.79: Dffirentiate the functions in 69 through 88.
 6.80: Dffirentiate the functions in 69 through 88.
 6.81: Dffirentiate the functions in 69 through 88.
 6.82: Dffirentiate the functions in 69 through 88.
 6.83: Dffirentiate the functions in 69 through 88.
 6.84: Dffirentiate the functions in 69 through 88.
 6.85: Dffirentiate the functions in 69 through 88.
 6.86: Dffirentiate the functions in 69 through 88.
 6.87: Dffirentiate the functions in 69 through 88.
 6.88: Dffirentiate the functions in 69 through 88.
 6.89: Evaluate the integrals in 89 through 108.
 6.90: Evaluate the integrals in 89 through 108.
 6.91: Evaluate the integrals in 89 through 108.
 6.92: Evaluate the integrals in 89 through 108.
 6.93: Evaluate the integrals in 89 through 108.
 6.94: Evaluate the integrals in 89 through 108.
 6.95: Evaluate the integrals in 89 through 108.
 6.96: Evaluate the integrals in 89 through 108.
 6.97: Evaluate the integrals in 89 through 108.
 6.98: Evaluate the integrals in 89 through 108.
 6.99: Evaluate the integrals in 89 through 108.
 6.100: Evaluate the integrals in 89 through 108.
 6.101: Evaluate the integrals in 89 through 108.
 6.102: Evaluate the integrals in 89 through 108.
 6.103: Evaluate the integrals in 89 through 108.
 6.104: Evaluate the integrals in 89 through 108.
 6.105: Evaluate the integrals in 89 through 108.
 6.106: Evaluate the integrals in 89 through 108.
 6.107: Evaluate the integrals in 89 through 108.
 6.108: Evaluate the integrals in 89 through 108.
 6.109: Find the volume generated by revolving around the yaxis the region...
 6.110: Find the volume generated by revolving around the ya,ris rhe regio...
 6.111: Use Eqs. (35) thrcugh (38) of Section 6.9 to show that tat corh Lr ...
 6.112: Show that x"(t) = k2x(t) if ,r(t) : A cosh.t/ + B sinhft, where A a...
 6.113: Use Newton's method to find the least positive solution of the equa...
 6.114: (a) Verify by differentiation that I r"r, d, =sin] r(tanxl + c. J ...
 6.115: Figure 6.MP3 shows the graphs of /(x) : yt/2, g(x) = lnr, and D(.t)...
Solutions for Chapter 6: Calculus:Early Transcendentals 7th Edition
Full solutions for Calculus:Early Transcendentals  7th Edition
ISBN: 9780131569898
Solutions for Chapter 6
Get Full SolutionsSince 115 problems in chapter 6 have been answered, more than 9228 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. Chapter 6 includes 115 full stepbystep solutions. Calculus:Early Transcendentals was written by and is associated to the ISBN: 9780131569898.

Additive identity for the complex numbers
0 + 0i is the complex number zero

Arc length formula
The length of an arc in a circle of radius r intercepted by a central angle of u radians is s = r u.

Cardioid
A limaçon whose polar equation is r = a ± a sin ?, or r = a ± a cos ?, where a > 0.

Central angle
An angle whose vertex is the center of a circle

Compounded annually
See Compounded k times per year.

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

Equation
A statement of equality between two expressions.

Expanded form of a series
A series written explicitly as a sum of terms (not in summation notation).

Heron’s formula
The area of ¢ABC with semiperimeter s is given by 2s1s  a21s  b21s  c2.

Lower bound for real zeros
A number c is a lower bound for the set of real zeros of ƒ if ƒ(x) Z 0 whenever x < c

Opposite
See Additive inverse of a real number and Additive inverse of a complex number.

Polynomial function
A function in which ƒ(x)is a polynomial in x, p. 158.

Projection of u onto v
The vector projv u = au # vƒvƒb2v

Pythagorean
Theorem In a right triangle with sides a and b and hypotenuse c, c2 = a2 + b2

Reflection across the xaxis
x, y and (x,y) are reflections of each other across the xaxis.

Solve a triangle
To find one or more unknown sides or angles of a triangle

Standard form of a polar equation of a conic
r = ke 1 e cos ? or r = ke 1 e sin ? ,

Symmetric property of equality
If a = b, then b = a

Trigonometric form of a complex number
r(cos ? + i sin ?)

Zero of a function
A value in the domain of a function that makes the function value zero.