Calculus Examples

$lim_{x \to π} \frac{\tan (x)}{x}$

Step 1

Split the limit using the Limits Quotient Rule on the limit as $x$ approaches $π$ .

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

Step 2

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

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

Step 3

Evaluate the limits by plugging in $π$ for all occurrences of $x$ .

Tap for more steps...

Step 3.1

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

$\frac{\tan (π)}{lim_{x \to π} x}$

Step 3.2

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

$\frac{\tan (π)}{π}$

Step 4

Simplify the answer.

Tap for more steps...

Step 4.1

Simplify the numerator.

Tap for more steps...

Step 4.1.1

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because tangent is negative in the second quadrant.

$\frac{- \tan (0)}{π}$

Step 4.1.2

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

$\frac{- 0}{π}$

Step 4.1.3

Multiply $- 1$ by $0$ .

$\frac{0}{π}$

Step 4.2

Divide $0$ by $π$ .

$0$