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

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Presentation transcript:

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

REVIEW: ALGEBRA is a ________________________ machine that ___________________ a function ___________ a point. CALCULUS is a ________________________ machine that ___________________________ a function ___________ a point

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: if Therefore: a) 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 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