Calculus Examples

$lim_{x \to - \frac{π}{2}} 2 \sec (2 x)$

Step 1

Evaluate the limit.

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Step 1.1

Move the term $2$ outside of the limit because it is constant with respect to $x$ .

$2 lim_{x \to - \frac{π}{2}} \sec (2 x)$

Step 1.2

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

$2 \sec (lim_{x \to - \frac{π}{2}} 2 x)$

Step 1.3

Move the term $2$ outside of the limit because it is constant with respect to $x$ .

$2 \sec (2 lim_{x \to - \frac{π}{2}} x)$

Step 2

Evaluate the limit of $x$ by plugging in $- \frac{π}{2}$ for $x$ .

$2 \sec (2 (- \frac{π}{2}))$

Step 3

Simplify the answer.

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Step 3.1

Cancel the common factor of $2$ .

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Step 3.1.1

Move the leading negative in $- \frac{π}{2}$ into the numerator.

$2 \sec (2 \frac{- π}{2})$

Step 3.1.2

Cancel the common factor.

$2 \sec (2 \frac{- π}{2})$

Step 3.1.3

Rewrite the expression.

$2 \sec (- π)$

Step 3.2

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.

$2 (- \sec (0))$

Step 3.3

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

$2 (- 1 \cdot 1)$

Step 3.4

Multiply $2 (- 1 \cdot 1)$ .

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Step 3.4.1

Multiply $- 1$ by $1$ .

$2 \cdot - 1$

Step 3.4.2

Multiply $2$ by $- 1$ .

$- 2$