The problem is to evaluate the limit using la'hospital rule..
$\displaystyle \lim_{x\rightarrow a} \left ( 2-\frac{x}{a} \right )^{tan\frac{\pi x}{2a}$
Soln.
Let, y = $\displaystyle \lim_{x\rightarrow a} \left ( 2-\frac{x}{a} \right )^{tan\frac{\pi x}{2a}}$
logy = $\displaystyle \lim_{x\rightarrow a} tan\frac{\pi x}{2a}\log \left (2-\frac{x}{a} \right )$
after applying La'Hospital rule, i gt this,
logy = $\displaystyle \frac{\pi}{2} \lim_{x\rightarrow a} sec^{2}\frac{\pi x}{2a}.tan\frac{\pi x}{2a}$
....i gt stuck in this step coz i gt repeatedly 0/0 form..n pliz suggest how do i write all these mathematical equations in faster and efficeint way, is there any software to make it possible???