 5.4.1: In Exercises 14, write tiie exponential equation as a logarith mi...
 5.4.2: In Exercises 14, write tiie exponential equation as a logarith mi...
 5.4.3: In Exercises 14, write tiie exponential equation as a logarith mi...
 5.4.4: In Exercises 14, write tiie exponential equation as a logarith mi...
 5.4.5: In Exercises 518, solve for .v accurate to three decimal places. '...
 5.4.6: In Exercises 518, solve for .v accurate to three decimal places. f...
 5.4.7: In Exercises 518, solve for .v accurate to three decimal places. e...
 5.4.8: In Exercises 518, solve for .v accurate to three decimal places. 4...
 5.4.9: In Exercises 518, solve for .v accurate to three decimal places. 9...
 5.4.10: In Exercises 518, solve for .v accurate to three decimal places. ...
 5.4.11: In Exercises 518, solve for .v accurate to three decimal places.50...
 5.4.12: In Exercises 518, solve for .v accurate to three decimal places. 2...
 5.4.13: In Exercises 518, solve for .v accurate to three decimal places. I...
 5.4.14: In Exercises 518, solve for .v accurate to three decimal places.In...
 5.4.15: In Exercises 518, solve for .v accurate to three decimal places. l...
 5.4.16: In Exercises 518, solve for .v accurate to three decimal places. I...
 5.4.17: In Exercises 518, solve for .v accurate to three decimal places.hi...
 5.4.18: In Exercises 518, solve for .v accurate to three decimal places.ln...
 5.4.19: In Exercises 1922, sketch the graph of the function. y = (?>
 5.4.20: In Exercises 1922, sketch the graph of the function. y = {e'
 5.4.21: In Exercises 1922, sketch the graph of the function. y = e''
 5.4.22: In Exercises 1922, sketch the graph of the function.y = f''
 5.4.23: Use a graphing utility to grapli/(.v) = c' and the given function i...
 5.4.24: U.se a graphing utility to graph the function. Use the graph to det...
 5.4.25: In Exercises 2528, match the equation with the correct graph. ,\ss...
 5.4.26: In Exercises 2528, match the equation with the correct graph. ,\ss...
 5.4.27: In Exercises 2528, match the equation with the correct graph. ,\ss...
 5.4.28: In Exercises 2528, match the equation with the correct graph. ,\ss...
 5.4.29: In Exercises 2932, illustrate that the functions are inverses of e...
 5.4.30: In Exercises 2932, illustrate that the functions are inverses of e...
 5.4.31: In Exercises 2932, illustrate that the functions are inverses of e...
 5.4.32: In Exercises 2932, illustrate that the functions are inverses of e...
 5.4.33: Graphical Analysis Use a graphing utility to graph fix) = I + and ,...
 5.4.34: Conjecture Use the result of E.xercise 33 to make a conjectiu'c abo...
 5.4.35: In Exercises 35 and 36, compare the given number with the number e....
 5.4.36: In Exercises 35 and 36, compare the given number with the number e....
 5.4.37: In Exercises 37 and 38, tlud the slope of the tangent line to the g...
 5.4.38: In Exercises 37 and 38, tlud the slope of the tangent line to the g...
 5.4.39: In Exercises 3958, find the derivative (if the I'unction. / (a) = ('
 5.4.40: In Exercises 3958, find the derivative (if the I'unction. fix) = c''
 5.4.41: In Exercises 3958, find the derivative (if the I'unction. V = f'...
 5.4.42: In Exercises 3958, find the derivative (if the I'unction. \' =
 5.4.43: In Exercises 3958, find the derivative (if the I'unction.V = f^
 5.4.44: In Exercises 3958, find the derivative (if the I'unction. V = xe~'
 5.4.45: In Exercises 3958, find the derivative (if the I'unction. (/) = i...
 5.4.46: In Exercises 3958, find the derivative (if the I'unction. ail) = c...
 5.4.47: In Exercises 3958, find the derivative (if the I'unction. . V = ln...
 5.4.48: In Exercises 3958, find the derivative (if the I'unction.8. = '"l .
 5.4.49: In Exercises 3958, find the derivative (if the I'unction. V = Ind +
 5.4.50: In Exercises 3958, find the derivative (if the I'unction.1,1 '' + ...
 5.4.51: In Exercises 3958, find the derivative (if the I'unction. y = 2 e1...
 5.4.52: In Exercises 3958, find the derivative (if the I'unction. ^,\ _ e'
 5.4.53: In Exercises 3958, find the derivative (if the I'unction. > = Ac'...
 5.4.54: In Exercises 3958, find the derivative (if the I'unction. V = Ac''...
 5.4.55: In Exercises 3958, find the derivative (if the I'unction./ (a I = ...
 5.4.56: In Exercises 3958, find the derivative (if the I'unction./ (a) = C...
 5.4.57: In Exercises 3958, find the derivative (if the I'unction.\' = c'(s...
 5.4.58: In Exercises 3958, find the derivative (if the I'unction. V = hit''
 5.4.59: In Exercises 59 and 60, use hiiplicit differentiation to find dyjdx...
 5.4.60: In Exercises 59 and 60, use hiiplicit differentiation to find dyjdx...
 5.4.61: In Exercises 61 and 62, find the second derivative of the fnnction....
 5.4.62: In Exercises 61 and 62, find the second derivative of the fnnction....
 5.4.63: In Exercises 63 and 64, show that the function y = /(v) is a soluti...
 5.4.64: In Exercises 63 and 64, show that the function y = /(v) is a soluti...
 5.4.65: In Exercises 6572, find the extrenia and the points of intlectlon ...
 5.4.66: In Exercises 6572, find the extrenia and the points of intlectlon ...
 5.4.67: In Exercises 6572, find the extrenia and the points of intlectlon ...
 5.4.68: In Exercises 6572, find the extrenia and the points of intlectlon ...
 5.4.69: In Exercises 6572, find the extrenia and the points of intlectlon ...
 5.4.70: In Exercises 6572, find the extrenia and the points of intlectlon ...
 5.4.71: In Exercises 6572, find the extrenia and the points of intlectlon ...
 5.4.72: In Exercises 6572, find the extrenia and the points of intlectlon ...
 5.4.73: Area Find the area of the largest rectangle that can be inscribed u...
 5.4.74: Area Pcrlorm the lollowing steps to lind the maxinium area of the r...
 5.4.75: Verif\ that llic fmictinn a > 0. b > 0. Z. > increases at a maximum...
 5.4.76: Find the point on the graph of v = t'"' where the normal line to th...
 5.4.77: Find, to three decimal places, the \alue of v such that ('" ' = .V....
 5.4.78: 78. 1 + ac'"' increases at a maximum rate when y = L/2. Find the p...
 5.4.79: Wriliiiti Consider the function 1 + c'' (a) Use a graphing ulilit>'...
 5.4.80: Harmonic Motion Tiie displacement lioni etiinliliriuni ot a mass os...
 5.4.81: Modeling Data A meteorologist measures the atmospheric pressure P (...
 5.4.82: Modeling Data A 1994 Chevrolet Camaio coupe with a 6cylinder engin...
 5.4.83: Linear and Quadratic Approximations In Exercises 8.^ and 84, use a ...
 5.4.84: Linear and Quadratic Approximations In Exercises 8.^ and 84, use a ...
 5.4.85: Finding a Pattern Use a graphing uliliU to compare the graph of the...
 5.4.86: Identity the pattern of successue polsnoniials m Exercise 85. Exten...
 5.4.87: In Kxercises 87108. find or evaluate the integral. c^'(5)
 5.4.88: In Kxercises 87108. find or evaluate the integral. c '{4x')ilx
 5.4.89: In Kxercises 87108. find or evaluate the integral. 1
 5.4.90: In Kxercises 87108. find or evaluate the integral. <' ',/v
 5.4.91: In Kxercises 87108. find or evaluate the integral. \c '' il\
 5.4.92: In Kxercises 87108. find or evaluate the integral. .v^c ' ' dx
 5.4.93: In Kxercises 87108. find or evaluate the integral. ''~;
 5.4.94: In Kxercises 87108. find or evaluate the integral. J x^ '^
 5.4.95: In Kxercises 87108. find or evaluate the integral. J.;.'^
 5.4.96: In Kxercises 87108. find or evaluate the integral. , '''\ dx
 5.4.97: In Kxercises 87108. find or evaluate the integral. J.;.
 5.4.98: In Kxercises 87108. find or evaluate the integral. vc ''
 5.4.99: In Kxercises 87108. find or evaluate the integral. e ' ^ ' 1  e>'...
 5.4.100: In Kxercises 87108. find or evaluate the integral. "'""' ' dx ( + c
 5.4.101: In Kxercises 87108. find or evaluate the integral. ,' + e'
 5.4.102: In Kxercises 87108. find or evaluate the integral. "2c>  2.'' ,
 5.4.103: In Kxercises 87108. find or evaluate the integral. '^dx
 5.4.104: In Kxercises 87108. find or evaluate the integral. f^^..
 5.4.105: In Kxercises 87108. find or evaluate the integral. '^dx ^" " ' CO...
 5.4.106: In Kxercises 87108. find or evaluate the integral. j.^cL :, ,_,,. ...
 5.4.107: In Kxercises 87108. find or evaluate the integral.t''Man(f')(/.v
 5.4.108: In Kxercises 87108. find or evaluate the integral. ln(c' ')(/v
 5.4.109: In Exercises 109 and 110. solve the differential equation. ^ = .V."
 5.4.110: In Exercises 109 and 110. solve the differential equation. ^ = ((^'...
 5.4.111: In Exercise.s 111 and 112. find tht particular solution that satisf...
 5.4.112: In Exercise.s 111 and 112. find tht particular solution that satisf...
 5.4.113: Slope Fields In Exerci.ses 1 13 and 114. a differential equation, a...
 5.4.114: Slope Fields In Exerci.ses 1 13 and 114. a differential equation, a...
 5.4.115: Xrea In F^xercises 115118, find the area of the region hounded by ...
 5.4.116: Xrea In F^xercises 115118, find the area of the region hounded by ...
 5.4.117: Xrea In F^xercises 115118, find the area of the region hounded by ...
 5.4.118: Xrea In F^xercises 115118, find the area of the region hounded by ...
 5.4.119: Gi\cn the exponential tnncluin fix) = c'. show that a) fill  I') (...
 5.4.120: Approxiinate each integral using the Midpoint Rule, the Trapezoidal...
 5.4.121: Probability A car battery has an average lifetime of 48 months with...
 5.4.122: Probability The median waiting time (in minutes) for people wailing...
 5.4.123: Gi\en f' > 1 for .v > 0. it follows that c' dl > \ I ill ^ Perform ...
 5.4.124: Modeling Data .\ \al\e on a storage tank is opened for 4 hours to r...
 5.4.125: In your own words, state the properties of the natural exponential ...
 5.4.126: Describe the relationship between the graph of /'(.v) = In.v and ,i...
 5.4.127: Is there a function /' such that / (,v) = / '(.v)'' If so. identify...
 5.4.128: Without integrating, state the integration formula you can use to i...
 5.4.129: Explain wh_\  c ' dx > (J
 5.4.130: Prove that'
 5.4.131: Let/(.v) In.v V (a) Graph / on (0. ^) and show that / is strictly ...
Solutions for Chapter 5.4: Exponential Functions: Differentiation and Integration
Full solutions for Calculus of A Single Variable  7th Edition
ISBN: 9780618149162
Solutions for Chapter 5.4: Exponential Functions: Differentiation and Integration
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Calculus of A Single Variable, edition: 7. Chapter 5.4: Exponential Functions: Differentiation and Integration includes 131 full stepbystep solutions. Calculus of A Single Variable was written by and is associated to the ISBN: 9780618149162. Since 131 problems in chapter 5.4: Exponential Functions: Differentiation and Integration have been answered, more than 25431 students have viewed full stepbystep solutions from this chapter.

Average velocity
The change in position divided by the change in time.

Branches
The two separate curves that make up a hyperbola

Coefficient
The real number multiplied by the variable(s) in a polynomial term

Control
The principle of experimental design that makes it possible to rule out other factors when making inferences about a particular explanatory variable

Degree of a polynomial (function)
The largest exponent on the variable in any of the terms of the polynomial (function)

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

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

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

Implied domain
The domain of a function’s algebraic expression.

Inductive step
See Mathematical induction.

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

Lower bound of f
Any number b for which b < ƒ(x) for all x in the domain of ƒ

Measure of center
A measure of the typical, middle, or average value for a data set

Plane in Cartesian space
The graph of Ax + By + Cz + D = 0, where A, B, and C are not all zero.

Polar axis
See Polar coordinate system.

Polar equation
An equation in r and ?.

Positive angle
Angle generated by a counterclockwise rotation.

Solve by elimination or substitution
Methods for solving systems of linear equations.

Upper bound for real zeros
A number d is an upper bound for the set of real zeros of ƒ if ƒ(x) ? 0 whenever x > d.

Wrapping function
The function that associates points on the unit circle with points on the real number line