 5.1: The graph of is shown. Is onetoone? Explain.
 5.2: The graph of is given. (a) Why is onetoone? (b) Estimate the valu...
 5.3: Suppose f is onetoone, , and . Find (a) and (b) .
 5.4: Find the inverse function of
 5.5: Sketch a rough graph of the function without using a calculator. y ...
 5.6: Sketch a rough graph of the function without using a calculator. y ex
 5.7: Sketch a rough graph of the function without using a calculator. y ...
 5.8: Sketch a rough graph of the function without using a calculator. y ...
 5.9: Sketch a rough graph of the function without using a calculator. y ...
 5.10: Let . For large values of , which of the functions , , and has the ...
 5.11: Find the exact value of each expression.
 5.12: Find the exact value of each expression.
 5.13: Solve the equation for
 5.14: Solve the equation for
 5.15: Solve the equation for
 5.16: Solve the equation for
 5.17: Differentiate. y lnx ln x
 5.18: Differentiate. y emx cos nx
 5.19: Differentiate. y y ln sec
 5.20: Differentiate. y ln sec x
 5.21: Differentiate. y sarctan x
 5.22: Differentiate. y x cos1x
 5.23: Differentiate. f t t 2 ln t
 5.24: Differentiate. tt et1 et
 5.25: Differentiate. y 3x ln x
 5.26: Differentiate. y cos xx
 5.27: Differentiate. y x sinhx2
 5.28: Differentiate. xey y x sinhx2 y sin x
 5.29: Differentiate. h etan 2
 5.30: Differentiate. y arcsin 2x2
 5.31: Differentiate. y ln sin x y 10tan
 5.32: Differentiate. y 10tan
 5.33: Differentiate. log51 2x
 5.34: Differentiate. y ecos x cosex
 5.35: Differentiate. y y sin1ex sx 1 2 x5x 3
 5.36: Differentiate. y sin1ex
 5.37: Differentiate. y x tan14x
 5.38: Differentiate. y x 2 142x 133x 15
 5.39: Differentiate. y lncosh 3x
 5.40: Differentiate. y arctan(arcsin sx )
 5.41: Differentiate. y cosh1sinh x
 5.42: Differentiate. y x tanh1y cosh1sinh x sx
 5.43: Differentiate. cos(estan 3x )
 5.44: Show that dx 12 tan1x 14 lnx 12x2 1 11 x1 x2
 5.45: Find in terms of f x e f x tex tx
 5.46: Find in terms of f x tex
 5.47: Find in terms of f x ln tx
 5.48: Find in terms of f x tln x
 5.49: Find f x 2x
 5.50: Find f x ln2x
 5.51: Use mathematical induction to show that if , then
 5.52: Find an equation of the tangent to the curve at the point
 5.53: At what point on the curve is the tangent horizontal?
 5.54: If , find . Graph and on the same screen and comment.
 5.55: (a) Find an equation of the tangent to the curve that is parallel t...
 5.56: The function , where a, b, and K are positive constants and , is us...
 5.57: A bacteria culture contains 200 cells initially and grows at a rate...
 5.58: Cobalt60 has a halflife of 5.24 years. (a) Find the mass that rem...
 5.59: Let be the concentration of a drug in the bloodstream. As the body ...
 5.60: A cup of hot chocolate has temperature in a room kept at . After ha...
 5.61: Evaluate the limit.
 5.62: Evaluate the limit.
 5.63: Evaluate the limit.
 5.64: Evaluate the limit.
 5.65: Evaluate the limit.
 5.66: Evaluate the limit.
 5.67: Evaluate the limit.
 5.68: Evaluate the limit.
 5.69: Evaluate the limit.
 5.70: Evaluate the limit.
 5.71: Evaluate the limit.
 5.72: Evaluate the limit.
 5.73: Evaluate the limit.
 5.74: Evaluate the limit.
 5.75: Evaluate the limit.
 5.76: Evaluate the limit.
 5.77: Evaluate the integral.
 5.78: Evaluate the integral.
 5.79: Evaluate the integral.
 5.80: Evaluate the integral.
 5.81: Evaluate the integral.
 5.82: Evaluate the integral.
 5.83: Evaluate the integral.
 5.84: Evaluate the integral.
 5.85: Evaluate the integral.
 5.86: Evaluate the integral.
 5.87: Evaluate the integral.
 5.88: Evaluate the integral.
 5.90: What is the area of the largest rectangle in the first quadrant wit...
 5.91: What is the area of the largest triangle in the first quadrant with...
Solutions for Chapter 5: Inverse Functions: Exponential, Logarithmic, and Inverse Trigonometric Functions
Full solutions for Essential Calculus  2nd Edition
ISBN: 9781133112297
Solutions for Chapter 5: Inverse Functions: Exponential, Logarithmic, and Inverse Trigonometric Functions
Get Full SolutionsSummary of Chapter 5: Inverse Functions: Exponential, Logarithmic, and Inverse Trigonometric Functions
Here we investigate their properties, compute their derivatives, and use them to describe exponential growth and decay in biology, physics, chemistry, and other sciences. We also study the inverses of the trigonometric and hyperbolic functions. Finally we look at a method (l’Hospital’s Rule) for computing limits of such functions.
This expansive textbook survival guide covers the following chapters and their solutions. Since 90 problems in chapter 5: Inverse Functions: Exponential, Logarithmic, and Inverse Trigonometric Functions have been answered, more than 26588 students have viewed full stepbystep solutions from this chapter. Chapter 5: Inverse Functions: Exponential, Logarithmic, and Inverse Trigonometric Functions includes 90 full stepbystep solutions. Essential Calculus was written by and is associated to the ISBN: 9781133112297. This textbook survival guide was created for the textbook: Essential Calculus, edition: 2.

Addition principle of probability.
P(A or B) = P(A) + P(B)  P(A and B). If A and B are mutually exclusive events, then P(A or B) = P(A) + P(B)

Anchor
See Mathematical induction.

Arccosine function
See Inverse cosine function.

Event
A subset of a sample space.

Interval notation
Notation used to specify intervals, pp. 4, 5.

Logarithm
An expression of the form logb x (see Logarithmic function)

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

NINT (ƒ(x), x, a, b)
A calculator approximation to ?ab ƒ(x)dx

Period
See Periodic function.

Permutation
An arrangement of elements of a set, in which order is important.

Power rule of logarithms
logb Rc = c logb R, R 7 0.

Range of a function
The set of all output values corresponding to elements in the domain.

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.

Reflection
Two points that are symmetric with respect to a lineor a point.

Repeated zeros
Zeros of multiplicity ? 2 (see Multiplicity).

Standard form: equation of a circle
(x  h)2 + (y  k2) = r 2

Statistic
A number that measures a quantitative variable for a sample from a population.

symmetric about the xaxis
A graph in which (x, y) is on the graph whenever (x, y) is; or a graph in which (r, ?) or (r, ?, ?) is on the graph whenever (r, ?) is

Vertical line
x = a.