# Math Help - I have no clue how to solve this. (limit).

1. ## I have no clue how to solve this. (limit).

Find a value (a) such that:

$\lim_{x\rightarrow 0}\frac{\tan(ax+\frac{\pi}{4})-1}{x}=4$

Any ideas?

2. Originally Posted by integral
Find a value (a) such that:

$\lim_{x\rightarrow 0}\frac{\tan(ax+\frac{\pi}{4})-1}{x}=4$

Any ideas?
L'Hopital ...

$\displaystyle \lim_{x \to 0} \frac{a\sec^2(ax + \pi/4)}{1} = 4$

$a = 2$

3. Originally Posted by integral
Find a value (a) such that:

$\lim_{x\rightarrow 0}\frac{\tan(ax+\frac{\pi}{4})-1}{x}=4$

Any ideas?
Evidently $a\ne0$. What if you let $ax=y$ then $x\to 0\implies y\to 0$ so that our limit becomes $\lim_{y\to 0}\frac{\tan(y+\frac{\pi}{4})-1}{\frac{y}{a}}=4\implies a=\frac{4}{\lim_{y\to0}\frac{\tan(y+\frac{\pi}{4})-1}{y}}$. I'm sure you can deal with that limit.