Calculus Examples

$lim_{z \to 0} 2 z + \csc (2 z) - 1$

Step 1

Consider the left sided limit.

$lim_{z \to 0^{-}} 2 z + \csc (2 z) - 1$

Step 2

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

$- \infty$

Step 3

Consider the right sided limit.

$lim_{z \to 0^{+}} 2 z + \csc (2 z) - 1$

Step 4

As the $z$ values approach $0$ 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.

$Does not exist$