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

$\infty$ .

$\infty$