Calculus Examples

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

Step 1

Split the limit using the Limits Quotient Rule on the limit as $x$ approaches $\frac{π}{4}$ .

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

Step 2

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

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

Step 3

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

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Step 3.1

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

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

Step 3.2

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

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

Step 4

Simplify the answer.

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Step 4.1

Multiply the numerator by the reciprocal of the denominator.

$\tan (\frac{π}{4}) \frac{4}{π}$

Step 4.2

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

$1 \frac{4}{π}$

Step 4.3

Multiply $\frac{4}{π}$ by $1$ .

$\frac{4}{π}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{4}{π}$

Decimal Form:

$1.27323954 \dots$