Calculus Examples

lim x \to - 3 tan (\frac{π x}{4})

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

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})

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

Step 1.2

Move the term

\frac{π}{4}

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

x

$x$ .

tan (\frac{π}{4} lim x \to - 3 x)

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

tan (\frac{π}{4} lim x \to - 3 x)

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

Step 2

Evaluate the limit of

x

$x$ by plugging in

- 3

$- 3$ for

x

$x$ .

tan (\frac{π}{4} \cdot - 3)

$\tan (\frac{π}{4} \cdot - 3)$

Step 3

Simplify the answer.

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Step 3.1

Combine

\frac{π}{4}

$\frac{π}{4}$ and

- 3

$- 3$ .

tan (\frac{π \cdot - 3}{4})

$\tan (\frac{π \cdot - 3}{4})$

Step 3.2

Move

- 3

$- 3$ to the left of

π

$π$ .

tan (\frac{- 3 \cdot π}{4})

$\tan (\frac{- 3 \cdot π}{4})$

Step 3.3

Move the negative in front of the fraction.

tan (- \frac{3 \cdot π}{4})

$\tan (- \frac{3 \cdot π}{4})$

Step 3.4

Add full rotations of

2 π

$2 π$ until the angle is greater than or equal to

0

$0$ and less than

2 π

$2 π$ .

tan (\frac{5 π}{4})

$\tan (\frac{5 π}{4})$

Step 3.5

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

tan (\frac{π}{4})

$\tan (\frac{π}{4})$

Step 3.6

The exact value of

tan (\frac{π}{4})

$\tan (\frac{π}{4})$ is

1

$1$ .

1

$1$

1

$1$