Question

Find the limit. Use l'Hospital's Rule where appropriate. If there is a more elementary method, consider using it. $$ \lim_{x \to 0} \sin(9x) \csc(7x) $$

Name: find the limit use lhospitals rule where appropriate if there is a more elementary method consider using it limx to 0 sin9x csc7x 00425
Uploaded: 2022-11-14T13:07:58-08:00
Duration: 2 min 37 s
Channel: Adi S
Description: find the limit use lhospitals rule where appropriate if there is a more elementary method consider using it limx to 0 sin9x csc7x 00425

          Find the limit. Use l'Hospital's Rule where appropriate. If there is a more elementary method, consider using it.
$$ \lim_{x \to 0} \sin(9x) \csc(7x) $$

Added by Tiffany H.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

11/14/2022

Step 1

First, let's rewrite the expression using the definition of cosecant: $\csc(\theta) = \frac{1}{\sin(\theta)}$. So, the expression becomes: $$ \lim_{x \to 0} \sin(9x) \frac{1}{\sin(7x)} = \lim_{x \to 0} \frac{\sin(9x)}{\sin(7x)} $$ Show more…

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Find the limit. Use l'Hospital's Rule where appropriate. If there is a more elementary method, consider using it. $$ \lim_{x \to 0} \sin(9x) \csc(7x) $$