Calculus Examples

$lim_{x \to \frac{1}{2}} x \sec (π x)$

Step 1

Consider the left sided limit.

$lim_{x \to {(\frac{1}{2})}^{-}} x \sec (π x)$

Step 2

As the $x$ values approach $\frac{1}{2}$ from the left, the function values increase without bound.

$\infty$

Step 3

Consider the right sided limit.

$lim_{x \to {(\frac{1}{2})}^{+}} x \sec (π x)$

Step 4

As the $x$ values approach $\frac{1}{2}$ from the right, the function values decrease without bound.

$- \infty$

Step 5

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

$Does not exist$