perfect study guide for math 221

8/4/2019 Perfect Study Guide for MATH 221

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Perfect Study Guide

With LAWSTUDENTNOTES

Midterm 1

Chapter 1-3

Ann Scheels


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Chapter 1: Functions

Section 1: Functions; Domain and Range

-

Y = f(x) Y equals f of x The symbol f represents the function Letter x is the independent variable representing the input value Letter y is the dependent variable representing the output value

- Function Definition: A function f from a set D to a set Y is a rule that assigns a unique

single element f(x)Y to each element xD

- Domain Definition: set D of all possible input values

- Range Definition: set of all values of f(x) as x varies throughout D

- Even Functions and Odd Functions: Symmetry A function y = f(x) is an Even function of x: if f(-x) = f(x) symmetric about y-axis Odd function of x: if f(-x) = -f(x) symmetric about origin

- Functions to Know:


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Section 2: Combining Functions; Shifting and Scaling Graphs

- Sum, Differences, Products, and Quotients

- Composite Functions Definition: If f and g are functions, the composite function f g is defined by

(f g)(x) = f(g(x)).

The domain of f g consists of the numbers x in the domain of g for which g(x)

lies in the domain of f.

- Shifting a Graph of a Function

- Scaling and Reflecting a Graph of a Function


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Section 3: Trigonometric Functions

- Angles- Six Basic Trigonometric Functions

-

Some Identifications

-


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Chapter 2: Limits and Continuity

Section 1: Rates of Change and Tangents to Curves

-

Average Rate of Change Definition: The average rate of change of y = f(x) with respect to x over the

interval [x1,x2] isy

=

(s)(1)

21=

(1h)(1)

h

Section 2: Limit of a Function and Limit Laws

- Limits of Function Values lim0 f(x) = L

- Limit Laws (L, M, k are real numbers)

- Sandwich Theorem


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Section 3: The Precise Definition of a Limit

- Definition of Limit

Section 4: One-Sided Limits

- One Sided Limits Right Hand Limit:

Left Hand Limit:

- Limits involving Sin

Section 5: Continuity

- Continuity Definition

- Continuity Test Definition

- Properties of Continuous Function


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- Intermediate Value Theorem

Section 6: Limits Involving Infinity; Asymptotes of Graphs

- Finite Limits

- Horizontal Asymptote


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Chapter 3: Differentiation

Section 1: Tangents and the Derivative at a Point

-

Derivative of a Function

Section 2: Derivative as a Function

-

Derivative of a Function

- Alternative Formula

- Differentiability Implies Continuity


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Section 3: Differentiation Rules

- Derivative of a Constant Function

- Power Rule for Positive Integers

- Constant Multiple Rule

- Derivative Sum Rule

- Derivative Product Rule

- Derivative Quotient Rule

Section 4: The Derivative as a Rate of Change

- Instantaneous Rate of Change

- Velocity, Speed, and Acceleration


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Section 5: Derivatives of Trigonometric Functions

- Functions to Memorize:

Section 6: The Chain Rule

- Chain Rule

perfect study guide for math 221

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