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