What is the limit of x->1 sinpi*x/(1-x)^2?
I want to solve it without using L'Hospital rule.
We are given to evaluate:
The first thing I am looking for is a way to apply the well-known result:
(1)
Seeing the denominator has as a factor, this takes me to . So we now have:
Now, let's use the substitution and we have:
Now let's finish rewriting the expression so we can apply (1):
Applying (1), we are left with:
Now, do we have:
?