Calculus Examples

$lim_{x \to \frac{π}{2}} x \sin (x)$

Step 1

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

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

Step 2

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

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

Step 3

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

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Step 3.1

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

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

Step 3.2

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

$\frac{π}{2} \cdot \sin (\frac{π}{2})$

Step 4

Simplify the answer.

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Step 4.1

The exact value of $\sin (\frac{π}{2})$ is $1$ .

$\frac{π}{2} \cdot 1$

Step 4.2

Multiply $\frac{π}{2}$ by $1$ .

$\frac{π}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{π}{2}$

Decimal Form:

$1.57079632 \dots$