Calculus Examples

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

Step 1

Consider the limit with the constant multiple $- 1$ removed.

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

Step 2

Since the numerator is positive and the denominator $\cos (x)$ approaches zero and is less than zero for $x$ near $\frac{π}{2}$ to the right, the function decreases without bound.

$- \infty$

Step 3

Since the function $\frac{2}{\cos (x)}$ approaches $- \infty$ , the negative constant $- 1$ times the function approaches $\infty$ .

$\infty$