Calculus Examples

$lim_{x \to 0} \tan (\frac{π}{4} \cdot \cos (\sin (x)))$

Step 1

Evaluate the limit.

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Step 1.1

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

$\tan (lim_{x \to 0} \frac{π}{4} \cdot \cos (\sin (x)))$

Step 1.2

Move the term $\frac{π}{4}$ outside of the limit because it is constant with respect to $x$ .

$\tan (\frac{π}{4} lim_{x \to 0} \cos (\sin (x)))$

Step 1.3

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

$\tan (\frac{π}{4} \cos (lim_{x \to 0} \sin (x)))$

Step 1.4

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

$\tan (\frac{π}{4} \cos (\sin (lim_{x \to 0} x)))$

Step 2

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

$\tan (\frac{π}{4} \cos (\sin (0)))$

Step 3

Simplify the answer.

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Step 3.1

The exact value of $\sin (0)$ is $0$ .

$\tan (\frac{π}{4} \cos (0))$

Step 3.2

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

$\tan (\frac{π}{4} \cdot 1)$

Step 3.3

Multiply $\frac{π}{4}$ by $1$ .

$\tan (\frac{π}{4})$

Step 3.4

The exact value of $\tan (\frac{π}{4})$ is $1$ .

$1$