Question

Evaluate lim_{x rightarrow 0} tan5x div x

Answer 1

\[\lim_{x \rightarrow 0} \tan5x \div x\]

Answer 2

Could you show how you got that please?

Answer 3

\[\lim_{u \rightarrow 0}\frac{\sin(u)}{u}=1\]
Do you know this?

Answer 4

This is true by squeeze thm
We will need this

Answer 5

Write in terms of sine and cosine functions

Answer 6

\[\lim_{x \rightarrow 0}\frac{\sin(5x)}{\cos(5x)} \cdot \frac{1}{x}\]
\[\lim_{x \rightarrow 0}\frac{\sin(5x)}{x} \cdot \frac{1}{\cos(5x)}\]