Calculus Examples

$lim_{x \to π} x \sec (x)$

Step 1

Split the limit using the Product of Limits Rule on the limit as

$x$ approaches

$π$ .

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

Step 2

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

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

Step 3

Evaluate the limits by plugging in

$π$ for all occurrences of

$x$ .

Tap for more steps...

Step 3.1

Evaluate the limit of

$x$ by plugging in

$π$ for

$x$ .

$π \cdot \sec (lim_{x \to π} x)$

Step 3.2

Evaluate the limit of

$x$ by plugging in

$π$ for

$x$ .

$π \cdot \sec (π)$

Step 4

Simplify the answer.

Tap for more steps...

Step 4.1

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.

$π \cdot (- \sec (0))$

Step 4.2

The exact value of

$\sec (0)$ is

$1$ .

$π \cdot (- 1 \cdot 1)$

Step 4.3

Multiply

$- 1$ by

$1$ .

$π \cdot - 1$

Step 4.4

Move

$- 1$ to the left of

$π$ .

$- 1 \cdot π$

Step 4.5

Rewrite

$- 1 π$ as

$- π$ .

$- π$

Step 5

The result can be shown in multiple forms.

Exact Form:

$- π$

Decimal Form:

$- 3.14159265 \dots$