Calculus Examples

$lim_{x \to 2 π} \sec (2 x)$

Step 1

Evaluate the limit.

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

$\sec (lim_{x \to 2 π} 2 x)$

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

$\sec (2 lim_{x \to 2 π} x)$

Step 2

Evaluate the limit of $x$ by plugging in $2 π$ for $x$ .

$\sec (2 (2 π))$

Step 3

Simplify the answer.

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Multiply $2$ by $2$ .

$\sec (4 π)$

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

$\sec (0)$

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

$1$