`lim_(x->0) sin^-1(x)/x` Find the limit. Use l’Hospital’s Rule where appropriate. If there is a more elementary method, consider using it. If l’Hospital’s Rule doesn’t apply,...

`lim_(x->0) sin^-1(x)/x` Find the limit. Use l’Hospital’s Rule where appropriate. If there is a more elementary method, consider using it. If l’Hospital’s Rule doesn’t apply, explain why.

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Textbook Question

Chapter 4, 4.4 - Problem 29 - Calculus: Early Transcendentals (7th Edition, James Stewart).
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nees101 | Student, Graduate | (Level 2) Adjunct Educator

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Given the limit `lim_{x->0}sin^(-1)(x/x)` . We have to find the limit.

Applying the limit we get,

`lim_{x->0}sin^(-1)(x/x)=lim_{x->0}sin^(-1)(1)=pi/2`

hence the limit is `pi/2`

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