Question

lim x->0
(tanx)/(4x)

Answer 1

\[\lim_{\Theta \rightarrow 0} \frac{ \tan \theta }{ 4\theta }\]

Answer 2

So, I would start by turning tan(theta) into sin/cos. Then keep in mind that we have a common trig limit that is taught, namely:
\[\lim_{x \rightarrow 0}\frac{ sinx }{ x }= 1\]So you want to manipulate what you have to try and match that common limit. Would you have an idea how to go about that?

Answer 3

\[\lim_{\theta \rightarrow 0} \frac{ 1 }{ 4\cos \theta }\]
Can I do that?

Answer 4

If I can, then 1/4

Answer 5

\(\bf \lim_{\theta \to 0} \cfrac{ \tan \theta }{ 4\theta }
\\ \quad \\
\cfrac{ \tan \theta }{ 4\theta }\implies \cfrac{\frac{sin(\theta)}{cos(\theta)}}{4\theta}\implies \cfrac{sin(\theta)}{cos(\theta)}\cdot \cfrac{1}{4\theta}
\\ \quad \\
\cfrac{sin(\theta)}{cos(\theta)4\theta}\implies \cfrac{sin(\theta)}{\theta}\cdot \cfrac{1}{4cos(\theta)}\)

Answer 6

Perfect. Thanks.

Answer 7

He did the work I was typing out, lol.

Answer 8

But you're correct, 1/4 :P

Answer 9

yw