Hey there

note: x approaches 0 on the limit, didn't know how to format the code

I was solving this problem on my textbook:

$\displaystyle lim((e^(x^2)-cos(x))/x^2)=?$

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:

$\displaystyle lim((e^(x^2)-cos(x))/x^2)=lim(e^(x^2))-lim(cos(x))/lim(x^2)$

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?

Thanks