Calculus Examples

$lim_{θ \to π} θ \sec (θ)$

Step 1

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

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

Step 2

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

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

Step 3

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

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Step 3.1

Evaluate the limit of $θ$ by plugging in $π$ for $θ$ .

$π \cdot \sec (lim_{θ \to π} θ)$

Step 3.2

Evaluate the limit of $θ$ by plugging in $π$ for $θ$ .

$π \cdot \sec (π)$

Step 4

Simplify the answer.

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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:

$- 3.14159265 \dots$