Calculus Examples

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

Step 1

Convert from $\frac{1}{\sin (x)}$ to $\csc (x)$ .

$lim_{x \to 0} \csc (x)$

Step 2

Consider the left sided limit.

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

Step 3

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

$- \infty$

Step 4

Consider the right sided limit.

$lim_{x \to 0^{+}} \csc (x)$

Step 5

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

$\infty$

Step 6

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

$Does not exist$