Calculus Examples

$lim_{x \to 0} e^{\sin (x)}$

Step 1

Evaluate the limit.

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Step 1.1

Move the limit into the exponent.

$e^{lim_{x \to 0} \sin (x)}$

Step 1.2

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

$e^{\sin (lim_{x \to 0} x)}$

Step 2

Evaluate the limit of $x$ by plugging in $0$ for $x$ .

$e^{\sin (0)}$

Step 3

Simplify the answer.

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Step 3.1

The exact value of $\sin (0)$ is $0$ .

$e^{0}$

Step 3.2

Anything raised to $0$ is $1$ .

$1$