Calculus Examples

$lim_{x \to 0} 1 - \frac{\cos (x)}{\sin (x)}$

Step 1

Convert from $\frac{\cos (x)}{\sin (x)}$ to $\cot (x)$ .

$lim_{x \to 0} 1 - \cot (x)$

Step 2

Consider the left sided limit.

$lim_{x \to 0^{-}} 1 - \cot (x)$

Step 3

As the $x$ values approach $0$ from the left, the function values increase without bound.

$\infty$

Step 4

Consider the right sided limit.

$lim_{x \to 0^{+}} 1 - \cot (x)$

Step 5

As the $x$ values approach $0$ from the right, the function values decrease without bound.

$- \infty$

Step 6

Since the left sided and right sided limits are not equal, the limit does not exist.

$Does not exist$