Question

evaluate the limit.
the limit as x approaches 0, (1/x^2)-csc^2(x)

Answer 1

is this
\[\lim_{x \rightarrow 0}\frac{1}{x^2}-\csc^2(x)\]

Answer 2

if so i think it is
\[-\frac{1}{3}\] are you allowed to use l'hopital?

Answer 3

yeah, that's how we're supposed to do it, but i'm not sure how to get to that answer

Answer 4

first of all get rid of that stupid cosecant and write
\[\frac{1}{x^2}-\frac{1}{\sin^2(x)}=\frac{\sin^2(x)-x^2}{x^2\sin^2(x)}\] now this is in the form
\[\frac{0}{0}\]so you can use l'hopital ,
of you course you need the chain rule and the product rule for both numerator and denominator, an i think you will have to do it twice

Answer 5

ok, thanks a lot!

Answer 6

yw