Question

lim x->0 3x-1+cos^2(x)/sin(x)

Answer 1

are you allowed l'hospital?

Answer 2

Yep L'hospital would make things easy :)

Answer 3

\[\lim_{x\to0}\frac{3x-1+\cos^2(x)}{\sin(x)}\]

\[\lim_{x\to0}\frac{3x-\sin^2(x)}{\sin(x)}\]

\[\lim_{x\to0}\left[3\frac{x}{\sin(x)}-\frac{\sin^2(x)}{\sin(x)}\right]\]

\[\lim_{x\to0}\left[3\frac{x}{\sin(x)}-\sin(x)\right]=3-0=3\]