Calculus Examples

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

Step 1

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

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

Step 2

Move the exponent $2$ from $x^{2}$ outside the limit using the Limits Power Rule.

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

Step 3

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

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

Step 4

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

Tap for more steps...

Step 4.1

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

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

Step 4.2

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

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

Step 5

Simplify the answer.

Tap for more steps...

Step 5.1

Apply the product rule to $\frac{π}{2}$ .

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

Step 5.2

Raise $2$ to the power of $2$ .

$\frac{π^{2}}{4} \cdot \cos (\frac{π}{2})$

Step 5.3

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

$\frac{π^{2}}{4} \cdot 0$

Step 5.4

Multiply $\frac{π^{2}}{4}$ by $0$ .

$0$