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AP CALCULUS

AP CALCULUS . 1002 Limits pt.2 One Sided Limits and Infinite Limits. REVIEW:. ALGEBRA is a ________________________ machine that ___________________ a function ___________ a point. f unction. e valuates. at.

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AP CALCULUS

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  1. AP CALCULUS 1002 Limits pt.2 One Sided Limits and Infinite Limits

  2. REVIEW: ALGEBRA is a ________________________ machine that ___________________ a function ___________ a point. function evaluates at CALCULUS is a ________________________ machine that ___________________________ a function ___________ a point limit that describes the behavior of near

  3. ONE-SIDED LIMITS

  4. 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: You MUST write the signs # to the right If a = 6 a+ =6.01 etc # to the left If a=6 a- = 5.99 etc USES: A. Existence of a Limit Theorem: The Limit of f(x) as x approaches a is L IFF You need to memorize this

  5. One - Sided Limits: cont EX: a) b) Therefore: DNE Does not exist EX: if a) b) Therefore:

  6. One - Sided Limits: cont 2 B. Limit at the end point of an Interval REM: Domain: Limit at Zero? DNE Why? Does not come from both sides but EX: Discuss the limit at the endpoints of f(x). Domain: REM :Number line analysis Limit from left Limit from right

  7. 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.

  8. 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. VAandlimit DNE EX: _______ Think-Don’t write 1.9 Think-Don’t write 2.1 Only time you don’t use # given (2) - +

  9. 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.

  10. Last Update: 08/31/10

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