Calculus Examples

$\frac{lim_{x \to \frac{π}{2}} 1 - 6 \cos (x)}{16 x}$

Step 1

Evaluate the limit.

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Step 1.1

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $\frac{π}{2}$ .

$\frac{lim_{x \to \frac{π}{2}} 1 - lim_{x \to \frac{π}{2}} 6 \cos (x)}{16 x}$

Step 1.2

Evaluate the limit of $1$ which is constant as $x$ approaches $\frac{π}{2}$ .

$\frac{1 - lim_{x \to \frac{π}{2}} 6 \cos (x)}{16 x}$

Step 1.3

Move the term $6$ outside of the limit because it is constant with respect to $x$ .

$\frac{1 - 6 lim_{x \to \frac{π}{2}} \cos (x)}{16 x}$

Step 1.4

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

$\frac{1 - 6 \cos (lim_{x \to \frac{π}{2}} x)}{16 x}$

Step 2

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

$\frac{1 - 6 \cos (\frac{π}{2})}{16 x}$

Step 3

Simplify the numerator.

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Step 3.1

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

$\frac{1 - 6 \cdot 0}{16 x}$

Step 3.2

Multiply $- 6$ by $0$ .

$\frac{1 + 0}{16 x}$

Step 3.3

Add $1$ and $0$ .

$\frac{1}{16 x}$