Calculus Examples

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

Step 1

Evaluate the limit.

Tap for more steps...

Step 1.1

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

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

Step 1.2

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

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

Step 2

Evaluate the limit of $x$ by plugging in $- 3$ for $x$ .

$\tan (\frac{π}{4} \cdot - 3)$

Step 3

Simplify the answer.

Tap for more steps...

Step 3.1

Combine $\frac{π}{4}$ and $- 3$ .

$\tan (\frac{π \cdot - 3}{4})$

Step 3.2

Move $- 3$ to the left of $π$ .

$\tan (\frac{- 3 \cdot π}{4})$

Step 3.3

Move the negative in front of the fraction.

$\tan (- \frac{3 \cdot π}{4})$

Step 3.4

Add full rotations of $2 π$ until the angle is greater than or equal to $0$ and less than $2 π$ .

$\tan (\frac{5 π}{4})$

Step 3.5

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant.

$\tan (\frac{π}{4})$

Step 3.6

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

$1$