Ch 5 Review
How do you find the inverse of a function?
f(x)=-1/2x+1
1. Place a y in for the "f(x)" function
y=-1/2x+1
2. Switch the x and y. ( because every (x, y) has a (y, x) partner
x=-1/2y+1
3. Solve for y.
x=-1/2y+1 multiply by 3 to get rid of the fr
Chapter 6 Terms and Formulas
Term/Property
Definition/Rule
Example
System of Linear
Equations
Is more than one equation
with two solutions. solving
a linear system is to use
the elimination method. In
the elimination method you
either add or subtract the
MAT 121/093
Test 2 Review/093 Assignment 2
Name_
Spring 2017 Answer key
Section_
Using the graph, determine the intervals on which the function is increasing or
decreasing, and any relative maxima and relative minima of the function.
1) f(x) = x3 - 3x2 +
MAT 121/093
Test 1 Review/Assignment 1
Name_
Section_
Use substitution to determine whether the given ordered pair is a solution of
the given equation.
1) (2, -5); 5x - 3y = 25
Answer: No
Find the intercepts and then graph the line.
2) 5x - 2y = 10
Answer
MAT 121/093
Test 2 Review/093 Assignment 2
Spring 2017
Using the graph, determine the intervals on which the function is increasing or
decreasing, and any relative maxima and relative minima of the function.
1) f(x) = x3 - 3x2 + 1
For the piecewise functi
MAT 121 College Algebra Test 4 review/093 assignment
CCD
Spring 2017
_
Find the inverse of the relation.
1) cfw_(11, 9), (-9, 18), (1, 19)
Using the horizontal-line test, determine whether the function is one-to-one.
2) -0.6x2 + 2x + 2
Determine whether t
tarl'e Tues/31V I; lb ' _ ' _
Section; 3 l Indenite Integrals
/"\
" * A inhaler l vat! U as
What is integration?
It is the Inverse O eration of differentiation.
MDTax -3x+a 900: 3
Remember what 1nverse operations do?
ECHO!) S"l)< 3 5"? 1300
So with integr
Math 125
Sec 12.3
Mars. W57, /
LHpitals Rule and the Indeterminate form 0/0
One-sided Limits and Limits at 00
LH6pitals Rule and the Indeterminate form 00/00
WW
Lets first look at what things are NOT the indeterminate form.
If:
lim fOC)
lim 106)
lint f(x)
Unit: Sequences and Series
Module: The Ratio and Root Tests
The Ratio Test
To apply the ratio test to a series
n =1
an , let
= lim
n
an +1 . an
If < 1, then the series converges absolutely. If > 1, then the series diverges. If = 1, then the test is inco
Unit: Sequences and Series
Module: Power Series Representations of Functions
Finding Power Series Representations by Differentiation
You can do calculus on a power series inside its interval of convergence. The derivative of the power series
n =0
an (
Unit: Sequences and Series
Module: Power Series Representations of Functions
Differentiation and Integration of Power Series
You can do calculus on a power series inside its interval of convergence. The derivative of the power series
n =0
an ( x c )n
Unit: Sequences and Series
Module: Power Series
Interval and Radius of Convergence
The interval of convergence of a power series is the collection of points for which the series converges. The radius of convergence of a power series is the distance betw
Unit: Sequences and Series
Module: Power Series
Definition of Power Series
The general form of a power series centered at x = c is a sequence of numbers that only depend on n.
n =0
an ( x c )n , where an is
All power series converge for x = c. If a pow
Unit: Sequences and Series
Module: Taylor and Maclaurin Series
Taylor Series
The Taylor series expansion of f ( x ) centered at x = c is
f ( n ) (c ) ( x c )n n! n =0
assuming that f ( x ) is differentiable an infinite number of times. For a given x, if
Unit: Sequences and Series
Module: Taylor and Maclaurin Polynomials
Maclaurin Polynomials
The Maclaurin polynomial of f (x ) is the Taylor polynomial of f (x ) centered at k f n0 n f (2) (0) 2 f ( k ) (0) k x = 0: x = f (0) (0) + f (1) (0)x + x +K+ x. 2 k
Unit: Sequences and Series
Module: Taylor and Maclaurin Polynomials
Taylor Polynomials
Higher-degree polynomial approximations result in more accurate representations. To find a Taylor polynomial, find all the necessary derivatives and evaluate them at
Unit: Sequences and Series
Module: Polynomial Approximations of Elementary Functions
Polynomial Approximation of Elementary Functions
Polynomials can approximate complicated functions. The tangent line approximation of f (x ) at x = c is y = f (c ) + f
The Root Test
To apply the nth root test to a series
n =1
an , let
= lim
n
n
an .
If < 1, then the series converges absolutely. If > 1, then the series diverges. If = 1, then the test is inconclusive. The nth root test is another way to see if the terms
Unit: Sequences and Series
Module: Power Series Representations of Functions
Finding Power Series Representations by Integration
You can do calculus on a power series inside its interval of convergence. The integral of the power series
n =0
an ( x c )n
Unit: Sequences and Series
Module: Infinite Series
[page 1 of 2]
Introduction to Infinite Series
Binary operations combine two values to yield a single result. You can add as many numbers as you want as long as you only have finitely many of them. Since