Question

Find the following limit
lim 3xcsc(2pi-x)
x->0+

Answer 1

usual gimmick is to write it as
\[3\lim_{x\to 0^+}\frac{\csc(2\pi-x)}{\frac{1}{x}}\] and use l'hopital's rule

Answer 2

So use product rule and go from there?

Answer 3

oh no
take the derivative top and bottom separately

Answer 4

top is -cotxcscx(2pi-x)(-1) = cotxcscx(2pi-x)
bottom is -1/x^2
Correct?