Question

Solve the following limit: EQUATION BELOW

Answer 1

\[\lim_{x \rightarrow 0} \cot(12x) -\frac{ 1 }{ 12x }\]

I am suposed to be using L'hopital's rule for this section of problems when possible.

Answer 2

i can get a common denominator and have \[\frac{ 12xcot(12x)-1 }{ 12x }\]

and that gives infinity/0, so i am stuck. I know the answer is suposed to be 0

Answer 3

wait.. does the top give infinity? 0*infinity-1=?

Answer 4

\[\lim_{x\to0}\left(\cot(12x)-\frac{1}{12x}\right)\\
\lim_{x\to0}\left(\frac{\cos(12x)}{\sin(12x)}-\frac{1}{12x}\right)\\
\lim_{x\to0}\frac{12x\cos(12x)-\sin(12x)}{12x\sin(12x)}\]