1003 Limits pt 2 One Sided Limits and

1003 Limits pt. 2 One Sided Limits and Infinite Limits AP CALCULUS

REVIEW: ALGEBRA is a ____________ machine that __________ a function ______ a point. CALCULUS is a ____________ machine that ______________ a function ______ a point

ONE-SIDED LIMITS

ONE-SIDED LIMITS General Idea: Behavior of a function as it approaches a point from a specific direction. (Left hand Limit - from values less than a) (Right Hand Limit - from values greater than a) Notation: USES: A. Existence of a Limit Theorem: The Limit of f(x) as x approaches a is L IFF

One - Sided Limits: cont EX: a) b) Therefore: EX: a) Therefore: if b)

One - Sided Limits: cont 2 B. Limit at the end point of an Interval REM: Domain: Limit at Zero? DNE why? But EX: Discuss the limit at the endpoints of f(x). Domain: REM : Number line analysis

Limits Review: PART 1(b): LOCAL BEHAVIOR REM: General Idea: Behavior of a function very near the point where INFINITE LIMITS General Idea: Behavior of a function near a Vertical Asymptote Warning: This is not a limit by the strict definition since is not a number.

INFINITE LIMITS Special Method: Start with Direct Substitution as always! This will produce an UNDEFINED fraction …. Not the Indeterminant form! Choose a number very close to the a on the left and right since plugging in a will always return the undefined fraction. EX: Think-Don’t write 1. 9 _______ Think-Don’t write 2. 1

Infinite Limits: cont Special Method: Start with Direct Substitution as always! This will produce an UNDEFINED fraction …. Not the Indeterminant form! Choose a number very close to the a on the left and right since plugging in a will always return the undefined fraction. EX: Think-Don’t write 1. 9 Think-Don’t write 2. 1 This I call a “Pseudo” Limit because it does describe the behavior on both sides BUT does not approach a SINGLE number.

Last Update: 08/31/10