Calculus Examples

$lim_{x \to 3} \tan (\frac{π x}{4})$

Step 1

Evaluate the limit.

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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.

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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

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.

$- \tan (\frac{π}{4})$

Step 3.4

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

$- 1 \cdot 1$

Step 3.5

Multiply $- 1$ by $1$ .

$- 1$