note: x approaches 0 on the limit, didn't know how to format the code
I was solving this problem on my textbook:
On my first method, I replaced cos(x) with 1-sin^2(x/2) and after some modifications, the result turned out to be 3/2 (which was also the result on the textbook).
On the other hand, I tried this solution:
From the limit laws we get:
we know that limcos(x) as x approaches 0 is 1, so we end up:
lim((e^(x^2)-1)/x^2), which is equal to 1. Could anyone explain where I'm wrong on my second method?