 7.1: How is the natural logarithm function defined as an integral? What ...
 7.2: What integrals lead to logarithms? Give examples.
 7.3: What are the integrals of tan x and cot x? sec x and csc x?
 7.4: How is the exponential function ex defined? What are its domain, ra...
 7.5: How are the functions ax and logax defined? Are there any restricti...
 7.6: How do you solve separable firstorder differential equations?
 7.7: What is the law of exponential change? How can it be derived from a...
 7.8: What are the six basic hyperbolic functions? Comment on their domai...
 7.9: What are the derivatives of the six basic hyperbolic functions? Wha...
 7.10: How are the inverse hyperbolic functions defined? Comment on their ...
 7.11: What integrals lead naturally to inverse hyperbolic functions?
Solutions for Chapter 7: University Calculus: Early Transcendentals 3rd Edition
Full solutions for University Calculus: Early Transcendentals  3rd Edition
ISBN: 9780321999580
Solutions for Chapter 7
Get Full SolutionsThis textbook survival guide was created for the textbook: University Calculus: Early Transcendentals, edition: 3. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 7 includes 11 full stepbystep solutions. University Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321999580. Since 11 problems in chapter 7 have been answered, more than 6438 students have viewed full stepbystep solutions from this chapter.

Commutative properties
a + b = b + a ab = ba

Cosecant
The function y = csc x

Dependent variable
Variable representing the range value of a function (usually y)

Inverse cosecant function
The function y = csc1 x

Inverse tangent function
The function y = tan1 x

n factorial
For any positive integer n, n factorial is n! = n.(n  1) . (n  2) .... .3.2.1; zero factorial is 0! = 1

Objective function
See Linear programming problem.

Parallel lines
Two lines that are both vertical or have equal slopes.

Projectile motion
The movement of an object that is subject only to the force of gravity

Quadratic regression
A procedure for fitting a quadratic function to a set of data.

Random numbers
Numbers that can be used by researchers to simulate randomness in scientific studies (they are usually obtained from lengthy tables of decimal digits that have been generated by verifiably random natural phenomena).

Rigid transformation
A transformation that leaves the basic shape of a graph unchanged.

Sinusoid
A function that can be written in the form f(x) = a sin (b (x  h)) + k or f(x) = a cos (b(x  h)) + k. The number a is the amplitude, and the number h is the phase shift.

Solve algebraically
Use an algebraic method, including paper and pencil manipulation and obvious mental work, with no calculator or grapher use. When appropriate, the final exact solution may be approximated by a calculator

Statute mile
5280 feet.

Sum identity
An identity involving a trigonometric function of u + v

Symmetric about the yaxis
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

Terminal point
See Arrow.

Third quartile
See Quartile.

Upper bound for ƒ
Any number B for which ƒ(x) ? B for all x in the domain of ƒ.