- 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 first-order 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
a + b = b + a ab = ba
The function y = csc x
Variable representing the range value of a function (usually y)
Inverse cosecant function
The function y = csc-1 x
Inverse tangent function
The function y = tan-1 x
For any positive integer n, n factorial is n! = n.(n - 1) . (n - 2) .... .3.2.1; zero factorial is 0! = 1
See Linear programming problem.
Two lines that are both vertical or have equal slopes.
The movement of an object that is subject only to the force of gravity
A procedure for fitting a quadratic function to a set of data.
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).
A transformation that leaves the basic shape of a graph unchanged.
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.
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
An identity involving a trigonometric function of u + v
Symmetric about the y-axis
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
Upper bound for ƒ
Any number B for which ƒ(x) ? B for all x in the domain of ƒ.