Calculus Examples

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

Step 1

Convert from $\frac{1}{\cos (x)}$ to $\sec (x)$ .

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

Step 2

Consider the left sided limit.

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

Step 3

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

$\infty$

Step 4

Consider the right sided limit.

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

Step 5

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

$\infty$