Calculus Examples

$lim_{x \to \frac{π}{4}} \tan (\frac{4 x}{3})$

Step 1

Evaluate the limit.

Tap for more steps...

Step 1.1

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

$\tan (lim_{x \to \frac{π}{4}} \frac{4 x}{3})$

Step 1.2

Move the term $\frac{4}{3}$ outside of the limit because it is constant with respect to $x$ .

$\tan (\frac{4}{3} lim_{x \to \frac{π}{4}} x)$

Step 2

Evaluate the limit of $x$ by plugging in $\frac{π}{4}$ for $x$ .

$\tan (\frac{4}{3} \cdot \frac{π}{4})$

Step 3

Simplify the answer.

Tap for more steps...

Step 3.1

Cancel the common factor of $4$ .

Tap for more steps...

Step 3.1.1

Cancel the common factor.

$\tan (\frac{4}{3} \cdot \frac{π}{4})$

Step 3.1.2

Rewrite the expression.

$\tan (\frac{1}{3} π)$

Step 3.2

Combine $\frac{1}{3}$ and $π$ .

$\tan (\frac{π}{3})$

Step 3.3

The exact value of $\tan (\frac{π}{3})$ is $\sqrt{3}$ .

$\sqrt{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\sqrt{3}$

Decimal Form:

$1.73205080 \dots$