2.5 Evaluating Limits Trig function.pptx - CALCULUS 12 2.5...

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2.5Evaluating Limits of Trigonometric FunctionsWhat is a the Squeeze Theorem?10/29/19CALCULUS 12
Lesson ObjectiveBy the end of the lesson, I will be able to…To learn evaluating the limit of a trigonometric function.
Squeeze TheoremSuppose the function f(x) is in between two other functions, g(x) and h(x)
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?(?)=sin??lim?→ ∞sin??Find:When we graph this function, the limit appears to be zero.1sin?1so for :?>01?sin??1?lim?→ ∞1?lim?→ ∞sin??lim?→∞1?0lim?→ ∞sin??0by the sandwich/squeeze/pinching theorem:limsi
Proof0<?<?2We are considering the area of triangle OAB, sector OABand triangle OAD????Δ<????sec???<??? ?Δsin?2<?2<???2sin?<?<???¿:sin?01<?sin?<1cos?1>sin??>cos??h????:cos?<sin??<1lim?0sin??=1???:cos?<sin??<1

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