Calculus Examples

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

Step 1

Move the limit inside the trig function because cosine is continuous.

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

Step 2

Evaluate the limit of $x$ by plugging in $\frac{π}{2}$ for $x$ .

$\frac{\cos (\frac{π}{2})}{1 - \sin (x)}$

Step 3

Simplify the answer.

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Step 3.1

The exact value of $\cos (\frac{π}{2})$ is $0$ .

$\frac{0}{1 - \sin (x)}$

Step 3.2

Divide $0$ by $1 - \sin (x)$ .

$0$