Calculus Examples

$lim_{x \to - π} \sec (x) \tan (x)$

Step 1

Split the limit using the Product of Limits Rule on the limit as $x$ approaches $- π$ .

$lim_{x \to - π} \sec (x) \cdot lim_{x \to - π} \tan (x)$

Step 2

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

$\sec (lim_{x \to - π} x) \cdot lim_{x \to - π} \tan (x)$

Step 3

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

$\sec (lim_{x \to - π} x) \cdot \tan (lim_{x \to - π} x)$

Step 4

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

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Step 4.1

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

$\sec (- π) \cdot \tan (lim_{x \to - π} x)$

Step 4.2

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

$\sec (- π) \cdot \tan (- π)$

Step 5

Simplify the answer.

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Step 5.1

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

$- \sec (0) \cdot \tan (- π)$

Step 5.2

The exact value of $\sec (0)$ is $1$ .

$- 1 \cdot 1 \cdot \tan (- π)$

Step 5.3

Multiply $- 1$ by $1$ .

$- 1 \cdot \tan (- π)$

Step 5.4

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.

$- 1 \cdot (- \tan (0))$

Step 5.5

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

$- 1 \cdot (- 0)$

Step 5.6

Multiply $- 1 (- 0)$ .

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Step 5.6.1

Multiply $- 1$ by $0$ .

$- 1 \cdot 0$

Step 5.6.2

Multiply $- 1$ by $0$ .

$0$