Question

does the limit of [ (cos x -1) / sin x ] as x ->0 exist?

Answer 1

\[\lim_{x \rightarrow 0}\frac{\cos(x)-1}{\sin(x)} \cdot \frac{\frac{1}{x}}{\frac{1}{x}}\]
the next step is the answer

Answer 2

so does the limit not exist because the right and left side limits are not equal to each other or because they are increasing without bound?

Answer 3

limit of top is 0
limit of bottom is 1
0/1=0

Answer 4

thanks!

Answer 5

you should know that
\[\lim_{x \rightarrow 0}\frac{\cos(x)-1}{x}=0 \& \lim_{x \rightarrow 0}\frac{\sin(x)}{x}=1\]