Calculus Examples

$\frac{lim_{x \to - 1} \tan (\frac{x + 1}{4})}{x}$

Step 1

Evaluate the limit.

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Step 1.1

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

$\frac{\tan (lim_{x \to - 1} \frac{x + 1}{4})}{x}$

Step 1.2

Move the term $\frac{1}{4}$ outside of the limit because it is constant with respect to $x$ .

$\frac{\tan (\frac{1}{4} lim_{x \to - 1} x + 1)}{x}$

Step 1.3

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $- 1$ .

$\frac{\tan (\frac{1}{4} (lim_{x \to - 1} x + lim_{x \to - 1} 1))}{x}$

Step 1.4

Evaluate the limit of $1$ which is constant as $x$ approaches $- 1$ .

$\frac{\tan (\frac{1}{4} (lim_{x \to - 1} x + 1))}{x}$

Step 2

Evaluate the limit of $x$ by plugging in $- 1$ for $x$ .

$\frac{\tan (\frac{1}{4} (- 1 + 1))}{x}$

Step 3

Simplify the answer.

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Step 3.1

Simplify the numerator.

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Step 3.1.1

Add $- 1$ and $1$ .

$\frac{\tan (\frac{1}{4} \cdot 0)}{x}$

Step 3.1.2

Multiply $\frac{1}{4}$ by $0$ .

$\frac{\tan (0)}{x}$

Step 3.1.3

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

$\frac{0}{x}$

Step 3.2

Divide $0$ by $x$ .

$0$