Calculus Examples

$\frac{lim_{x \to \frac{π}{2}} 2 \sin (x)}{3 x}$

Step 1

Evaluate the limit.

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Step 1.1

Move the term $2$ outside of the limit because it is constant with respect to $x$ .

$\frac{2 lim_{x \to \frac{π}{2}} \sin (x)}{3 x}$

Step 1.2

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

$\frac{2 \sin (lim_{x \to \frac{π}{2}} x)}{3 x}$

Step 2

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

$\frac{2 \sin (\frac{π}{2})}{3 x}$

Step 3

Simplify the answer.

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Step 3.1

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

$\frac{2 \cdot 1}{3 x}$

Step 3.2

Multiply $2$ by $1$ .

$\frac{2}{3 x}$