Calculus Examples

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

Step 1

Evaluate the limit.

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Step 1.1

Move the limit into the exponent.

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

Step 1.2

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

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

Step 2

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

$e^{\sin (\frac{π}{2})}$

Step 3

Simplify the answer.

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Step 3.1

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

$e^{1}$

Step 3.2

Simplify.

$e$

Step 4

The result can be shown in multiple forms.

Exact Form:

$e$

Decimal Form:

$2.71828182 \dots$