 5.4.1: In Exercises 116, solve for accurate to three decimal places.
 5.4.2: In Exercises 116, solve for accurate to three decimal places.
 5.4.3: In Exercises 116, solve for accurate to three decimal places.
 5.4.4: In Exercises 116, solve for accurate to three decimal places.
 5.4.5: In Exercises 116, solve for accurate to three decimal places.
 5.4.6: In Exercises 116, solve for accurate to three decimal places.
 5.4.7: In Exercises 116, solve for accurate to three decimal places.
 5.4.8: In Exercises 116, solve for accurate to three decimal places.
 5.4.9: In Exercises 116, solve for accurate to three decimal places.
 5.4.10: In Exercises 116, solve for accurate to three decimal places.
 5.4.11: In Exercises 116, solve for accurate to three decimal places.
 5.4.12: In Exercises 116, solve for accurate to three decimal places.
 5.4.13: In Exercises 116, solve for accurate to three decimal places.
 5.4.14: In Exercises 116, solve for accurate to three decimal places.
 5.4.15: In Exercises 116, solve for accurate to three decimal places.
 5.4.16: In Exercises 116, solve for accurate to three decimal places.
 5.4.17: In Exercises 1722, sketch the graph of the function.y ex l
 5.4.18: In Exercises 1722, sketch the graph of the function.y 1 2ex y
 5.4.19: In Exercises 1722, sketch the graph of the function.y ex 2
 5.4.20: In Exercises 1722, sketch the graph of the function.y ex1 y
 5.4.21: In Exercises 1722, sketch the graph of the function.y ex2
 5.4.22: In Exercises 1722, sketch the graph of the function.y ex 2 y
 5.4.23: Use a graphing utility to graph and the given function in the same ...
 5.4.24: Use a graphing utility to graph the function. Use the graph to dete...
 5.4.25: In Exercises 2528, match the equation with the correct graph. Assum...
 5.4.26: In Exercises 2528, match the equation with the correct graph. Assum...
 5.4.27: In Exercises 2528, match the equation with the correct graph. Assum...
 5.4.28: In Exercises 2528, match the equation with the correct graph. Assum...
 5.4.29: In Exercises 2932, illustrate that the functions are inverses of ea...
 5.4.30: In Exercises 2932, illustrate that the functions are inverses of ea...
 5.4.31: In Exercises 2932, illustrate that the functions are inverses of ea...
 5.4.32: In Exercises 2932, illustrate that the functions are inverses of ea...
 5.4.33: Use a graphing utility to graph and in the same viewing window. Wha...
 5.4.34: Use the result of Exercise 33 to make a conjecture about the value of
 5.4.35: In Exercises 35 and 36, compare the given number with the number Is...
 5.4.36: In Exercises 35 and 36, compare the given number with the number Is...
 5.4.37: In Exercises 37 and 38, find an equation of the tangent line to the...
 5.4.38: In Exercises 37 and 38, find an equation of the tangent line to the...
 5.4.39: In Exercises 39 60, find the derivative.
 5.4.40: In Exercises 39 60, find the derivative.
 5.4.41: In Exercises 39 60, find the derivative.
 5.4.42: In Exercises 39 60, find the derivative.
 5.4.43: In Exercises 39 60, find the derivative.
 5.4.44: In Exercises 39 60, find the derivative.
 5.4.45: In Exercises 39 60, find the derivative.
 5.4.46: In Exercises 39 60, find the derivative.
 5.4.47: In Exercises 39 60, find the derivative.
 5.4.48: In Exercises 39 60, find the derivative.
 5.4.49: In Exercises 39 60, find the derivative.
 5.4.50: In Exercises 39 60, find the derivative.
 5.4.51: In Exercises 39 60, find the derivative.
 5.4.52: In Exercises 39 60, find the derivative.
 5.4.53: In Exercises 39 60, find the derivative.
 5.4.54: In Exercises 39 60, find the derivative.
 5.4.55: In Exercises 39 60, find the derivative.
 5.4.56: In Exercises 39 60, find the derivative.
 5.4.57: In Exercises 39 60, find the derivative.
 5.4.58: In Exercises 39 60, find the derivative.
 5.4.59: In Exercises 39 60, find the derivative.
 5.4.60: In Exercises 39 60, find the derivative.
 5.4.61: In Exercises 61 68, find an equation of the tangent line to the gra...
 5.4.62: In Exercises 61 68, find an equation of the tangent line to the gra...
 5.4.63: In Exercises 61 68, find an equation of the tangent line to the gra...
 5.4.64: In Exercises 61 68, find an equation of the tangent line to the gra...
 5.4.65: In Exercises 61 68, find an equation of the tangent line to the gra...
 5.4.66: In Exercises 61 68, find an equation of the tangent line to the gra...
 5.4.67: In Exercises 61 68, find an equation of the tangent line to the gra...
 5.4.68: In Exercises 61 68, find an equation of the tangent line to the gra...
 5.4.69: In Exercises 69 and 70, use implicit differentiation to find dy/dx.
 5.4.70: In Exercises 69 and 70, use implicit differentiation to find dy/dx.
 5.4.71: In Exercises 71 and 72, find an equation of the tangent line to the...
 5.4.72: In Exercises 71 and 72, find an equation of the tangent line to the...
 5.4.73: In Exercises 73 and 74, find the second derivative of the function.
 5.4.74: In Exercises 73 and 74, find the second derivative of the function.
 5.4.75: In Exercises 7578, show that the function is a solution of the diff...
 5.4.76: In Exercises 7578, show that the function is a solution of the diff...
 5.4.77: In Exercises 7578, show that the function is a solution of the diff...
 5.4.78: In Exercises 7578, show that the function is a solution of the diff...
 5.4.79: fx ex ex 2 y
 5.4.80: fx ex ex 2 fx
 5.4.81: gx 1 2 ex2 2 2 f
 5.4.82: gx 1 2 ex3 2 2 gx
 5.4.83: fx x2ex g
 5.4.84: fx xex f
 5.4.85: gt 1 2 te 4 2x t f
 5.4.86: fx 2 e3x gt 1 2 te 4 2x t f
 5.4.87: Find the area of the largest rectangle that can be inscribed under ...
 5.4.88: Perform the following steps to find the maximum area of the rectang...
 5.4.89: Find a point on the graph of the function such that the tangent lin...
 5.4.90: Find the point on the graph of where the normal line to the curve p...
 5.4.91: The value of an item years after it is purchased is (a) Use a graph...
 5.4.92: The displacement from equilibrium of a mass oscillating on the end ...
 5.4.93: A meteorologist measures the atmospheric pressure (in kilograms per...
 5.4.94: The table lists the approximate values of a midsized sedan for the...
 5.4.95: In Exercises 95 and 96, use a graphing utility to graph the functio...
 5.4.96: In Exercises 95 and 96, use a graphing utility to graph the functio...
 5.4.97: In Exercises 97 and 98, find the exact value of and then approximat...
 5.4.98: In Exercises 97 and 98, find the exact value of and then approximat...
 5.4.99: In Exercises 99116, find the indefinite integral.
 5.4.100: In Exercises 99116, find the indefinite integral.
 5.4.101: In Exercises 99116, find the indefinite integral.
 5.4.102: In Exercises 99116, find the indefinite integral.
 5.4.103: In Exercises 99116, find the indefinite integral.
 5.4.104: In Exercises 99116, find the indefinite integral.
 5.4.105: In Exercises 99116, find the indefinite integral.
 5.4.106: In Exercises 99116, find the indefinite integral.
 5.4.107: In Exercises 99116, find the indefinite integral.
 5.4.108: In Exercises 99116, find the indefinite integral.
 5.4.109: In Exercises 99116, find the indefinite integral.
 5.4.110: In Exercises 99116, find the indefinite integral.
 5.4.111: In Exercises 99116, find the indefinite integral.
 5.4.112: In Exercises 99116, find the indefinite integral.
 5.4.113: In Exercises 99116, find the indefinite integral.
 5.4.114: In Exercises 99116, find the indefinite integral.
 5.4.115: In Exercises 99116, find the indefinite integral.
 5.4.116: In Exercises 99116, find the indefinite integral.
 5.4.117: In Exercises 117126, evaluate the definite integral. Use a graphing...
 5.4.118: In Exercises 117126, evaluate the definite integral. Use a graphing...
 5.4.119: In Exercises 117126, evaluate the definite integral. Use a graphing...
 5.4.120: In Exercises 117126, evaluate the definite integral. Use a graphing...
 5.4.121: In Exercises 117126, evaluate the definite integral. Use a graphing...
 5.4.122: In Exercises 117126, evaluate the definite integral. Use a graphing...
 5.4.123: In Exercises 117126, evaluate the definite integral. Use a graphing...
 5.4.124: In Exercises 117126, evaluate the definite integral. Use a graphing...
 5.4.125: In Exercises 117126, evaluate the definite integral. Use a graphing...
 5.4.126: In Exercises 117126, evaluate the definite integral. Use a graphing...
 5.4.127: In Exercises 127 and 128, solve the differential equation.dy dx xeax2
 5.4.128: In Exercises 127 and 128, solve the differential equation.dy dx ex ...
 5.4.129: In Exercises 129 and 130, find the particular solution that satisfi...
 5.4.130: In Exercises 129 and 130, find the particular solution that satisfi...
 5.4.131: In Exercises 131 and 132, a differential equation, a point, and a s...
 5.4.132: In Exercises 131 and 132, a differential equation, a point, and a s...
 5.4.133: In Exercises 133136, find the area of the region bounded by the gra...
 5.4.134: In Exercises 133136, find the area of the region bounded by the gra...
 5.4.135: In Exercises 133136, find the area of the region bounded by the gra...
 5.4.136: In Exercises 133136, find the area of the region bounded by the gra...
 5.4.137: In Exercises 137 and 138, approximate the integral using the Midpoi...
 5.4.138: In Exercises 137 and 138, approximate the integral using the Midpoi...
 5.4.139: A car battery has an average lifetime of 48 months with a standard ...
 5.4.140: The median waiting time (in minutes) for people waiting for service...
 5.4.141: The position function of a particle moving along the axis is where...
 5.4.142: A valve on a storage tank is opened for 4 hours to release a chemic...
 5.4.143: In your own words, state the properties of the natural exponential ...
 5.4.144: Is there a function such that If so, identify it.
 5.4.145: Without integrating, state the integration formula you can use to i...
 5.4.146: Consider the function (a) Use a graphing utility to graph (b) Write...
 5.4.147: Given for it follows that Perform this integration to derive the in...
 5.4.148: Describe the relationship between the graph of
 5.4.149: Find, to three decimal places, the value of such that (Use Newtons ...
 5.4.150: Find the value of such that the area bounded by the axis, and
 5.4.151: Verify that the function increases at a maximum rate when y L 2.
 5.4.152: Let (a) Graph on and show that is strictly decreasing on (b) Show t...
Solutions for Chapter 5.4: Exponential Functions: Differentiation and Integration
Full solutions for Calculus  9th Edition
ISBN: 9780547167022
Solutions for Chapter 5.4: Exponential Functions: Differentiation and Integration
Get Full SolutionsThis textbook survival guide was created for the textbook: Calculus , edition: 9. Since 152 problems in chapter 5.4: Exponential Functions: Differentiation and Integration have been answered, more than 61678 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 5.4: Exponential Functions: Differentiation and Integration includes 152 full stepbystep solutions. Calculus was written by and is associated to the ISBN: 9780547167022.

Amplitude
See Sinusoid.

Blind experiment
An experiment in which subjects do not know if they have been given an active treatment or a placebo

Blocking
A feature of some experimental designs that controls for potential differences between subject groups by applying treatments randomly within homogeneous blocks of subjects

Cofunction identity
An identity that relates the sine, secant, or tangent to the cosine, cosecant, or cotangent, respectively

Complex plane
A coordinate plane used to represent the complex numbers. The xaxis of the complex plane is called the real axis and the yaxis is the imaginary axis

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

Empty set
A set with no elements

Leibniz notation
The notation dy/dx for the derivative of ƒ.

Negative linear correlation
See Linear correlation.

Onetoone rule of logarithms
x = y if and only if logb x = logb y.

Order of an m x n matrix
The order of an m x n matrix is m x n.

Ordered pair
A pair of real numbers (x, y), p. 12.

Polar form of a complex number
See Trigonometric form of a complex number.

Power function
A function of the form ƒ(x) = k . x a, where k and a are nonzero constants. k is the constant of variation and a is the power.

Pythagorean identities
sin2 u + cos2 u = 1, 1 + tan2 u = sec2 u, and 1 + cot2 u = csc2 u

Rational function
Function of the form ƒ(x)/g(x) where ƒ(x) and g(x) are polynomials and g(x) is not the zero polynomial.

Right triangle
A triangle with a 90° angle.

Sample standard deviation
The standard deviation computed using only a sample of the entire population.

Sequence
See Finite sequence, Infinite sequence.

Square matrix
A matrix whose number of rows equals the number of columns.