- 8.1: What is the formula for integration by parts? Where does it come fr...
- 8.2: When applying the formula for integration by parts, how do you choo...
- 8.3: If an integrand is a product of the form sinnx cosmx, where m and n...
- 8.4: What substitutions are made to evaluate integrals of sin mx sin nx,...
- 8.5: What substitutions are sometimes used to transform integrals involv...
- 8.6: What restrictions can you place on the variables involved in the th...
- 8.7: What is the goal of the method of partial fractions?
- 8.8: When the degree of a polynomial (x) is less than the degree of a po...
- 8.9: How are integral tables typically used? What do you do if a par-tic...
- 8.10: What is a reduction formula? How are reduction formulas used? Give ...
- 8.11: How would you compare the relative merits of Simpsons Rule and the ...
- 8.12: What is an improper integral of Type I? Type II? How are the values...
Solutions for Chapter 8: University Calculus: Early Transcendentals 3rd Edition
Full solutions for University Calculus: Early Transcendentals | 3rd Edition
A function is bounded below if there is a number b such that b ? ƒ(x) for all x in the domain of f.
Combinations of n objects taken r at a time
There are nCr = n! r!1n - r2! such combinations,
Interest that becomes part of the investment
The factor Ae-a in an equation such as y = Ae-at cos bt
The process of utilizing general information to prove a specific hypothesis
Degree of a polynomial (function)
The largest exponent on the variable in any of the terms of the polynomial (function)
Horizontal Line Test
A test for determining whether the inverse of a relation is a function.
The line segment through the foci of an ellipse with endpoints on the ellipse
Natural exponential function
The function ƒ1x2 = ex.
A distribution of data shaped like the normal curve.
Quotient of complex numbers
a + bi c + di = ac + bd c2 + d2 + bc - ad c2 + d2 i
An equation found by regression and which can be used to predict unknown values.
Zeros of multiplicity ? 2 (see Multiplicity).
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 by elimination or substitution
Methods for solving systems of linear equations.
Sum of an infinite series
See Convergence of a series
The function y = tan x
A special form for a system of linear equations that facilitates finding the solution.
For real numbers a and b, exactly one of the following is true: a < b, a = b , or a > b.
A vector that specifies the motion of an object in terms of its speed and direction.