Calculus Examples

$\frac{lim_{x \to 0} \sin (\cos (8 x))}{\sec (5 x)}$

Step 1

Evaluate the limit.

Tap for more steps...

Step 1.1

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

$\frac{\sin (lim_{x \to 0} \cos (8 x))}{\sec (5 x)}$

Step 1.2

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

$\frac{\sin (\cos (lim_{x \to 0} 8 x))}{\sec (5 x)}$

Step 1.3

Move the term $8$ outside of the limit because it is constant with respect to $x$ .

$\frac{\sin (\cos (8 lim_{x \to 0} x))}{\sec (5 x)}$

Step 2

Evaluate the limit of $x$ by plugging in $0$ for $x$ .

$\frac{\sin (\cos (8 \cdot 0))}{\sec (5 x)}$

Step 3

Simplify the answer.

Tap for more steps...

Step 3.1

Rewrite $\sec (5 x)$ in terms of sines and cosines.

$\frac{\sin (\cos (8 \cdot 0))}{\frac{1}{\cos (5 x)}}$

Step 3.2

Multiply by the reciprocal of the fraction to divide by $\frac{1}{\cos (5 x)}$ .

$\sin (\cos (8 \cdot 0)) \cos (5 x)$

Step 3.3

Multiply $8$ by $0$ .

$\sin (\cos (0)) \cos (5 x)$

Step 3.4

The exact value of $\cos (0)$ is $1$ .

$\sin (1) \cos (5 x)$

Step 3.5

Evaluate $\sin (1)$ .

$0.0174524 \cos (5 x)$