Precalculus Examples

$lim_{x \to π} \csc (2 x)$

Step 1

Consider the left sided limit.

$lim_{x \to π^{-}} \csc (2 x)$

Step 2

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

$- \infty$

Step 3

Consider the right sided limit.

$lim_{x \to π^{+}} \csc (2 x)$

Step 4

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

$\infty$

Step 5

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

$Does not exist$