Chapter 1: Limit and Continuity
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Single Variable Calculus: Limit and Continuity
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Chapter 1: Limit and Contunity
Rates of Change and Limits
Average Rate of Change
Instantaneous Rate of Change
Definition of Limit
Situations where limits fail to exist
Jump
Grows too large to have a limit
Oscillates too much to have a limit
Finding Limits and One-Sided Limits
Properties of Limits
Theorem 1: Limit Rules
Theorem 2: Limits of Polynomials Can Be Found by Substitution
Theorem 3: Limits of Rational Functions Can Be Found by Substitution
Eliminate Zero Denominator
Sandwich Theorem
Two-Sided Limit
One-Sided Limit
Right-Hand Limit
Left-Hand Limit
Relation between One-sided and Two-sided limits
Limits Involving Infinity
Symbol: Infinity
Limits that approaches infinity and minus infinity
Rules for limits as x approaches infinity and minus infinity
Asymptotes
Horizontal Asymptote
x approaches (minus) infinity
Vertical Asymptote
x approaches values where denominator is zero
End Behavior Model
Oblique Asymptote
Continuity
Definition: Continuous Function
Continuity Test
1. f(c) exists
2. lim(x->c) f(x) exists
3. lim(x->c) f(x) = f(c)
Types of discontinuities
Jump discontinuity
Infinite discontinuity
Oscillating discontinuity
Properties of Continuous Function
Composite of Continuous Functions
The Intermediate Value Theorem for Continuous Functions
Tangent Lines
Definition for Tangent Lines
Slope and Tangent Line
Derivative at a point
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