Precalculus Examples

$lim_{x \to \frac{π}{2}} 3 e^{x} \cos (x)$

Step 1

Move the term $3$ outside of the limit because it is constant with respect to $x$ .

$3 lim_{x \to \frac{π}{2}} e^{x} \cos (x)$

Step 2

Split the limit using the Product of Limits Rule on the limit as $x$ approaches $\frac{π}{2}$ .

$3 lim_{x \to \frac{π}{2}} e^{x} \cdot lim_{x \to \frac{π}{2}} \cos (x)$

Step 3

Move the limit into the exponent.

$3 e^{lim_{x \to \frac{π}{2}} x} \cdot lim_{x \to \frac{π}{2}} \cos (x)$

Step 4

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

$3 e^{lim_{x \to \frac{π}{2}} x} \cdot \cos (lim_{x \to \frac{π}{2}} x)$

Step 5

Evaluate the limits by plugging in $\frac{π}{2}$ for all occurrences of $x$ .

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Step 5.1

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

$3 e^{\frac{π}{2}} \cdot \cos (lim_{x \to \frac{π}{2}} x)$

Step 5.2

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

$3 e^{\frac{π}{2}} \cdot \cos (\frac{π}{2})$

Step 6

Simplify the answer.

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Step 6.1

The exact value of $\cos (\frac{π}{2})$ is $0$ .

$3 e^{\frac{π}{2}} \cdot 0$

Step 6.2

Multiply $3 e^{\frac{π}{2}} \cdot 0$ .

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Step 6.2.1

Multiply $0$ by $3$ .

$0 e^{\frac{π}{2}}$

Step 6.2.2

Multiply $0$ by $e^{\frac{π}{2}}$ .

$0$