`lim_(x->0) x/(tan^-1(4x))` 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) x/(tan^-1(4x))` 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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Chapter 4, 4.4 - Problem 34 - 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}x/(tan^(-1)(4x))` . We have to find the limit value.

Applying the limit we get,

`lim_{x->0}x/(tan^(-1)(4x))=0/0`

So we use L'Hospital's rule to obtain,

`lim_{x->0}1/(1/(4^2+x^2))=lim_{x->0}16+x^2=16`

hence the limit is 16.

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