Calculus Examples

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

Step 1

Evaluate the limit.

Tap for more steps...

Step 1.1

Move the limit under the radical sign.

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

Step 1.2

Move the limit into the exponent.

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

Step 1.3

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

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

Step 1.4

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

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

Step 2

Evaluate the limit of $x$ by plugging in $2$ for $x$ .

$\sqrt{e^{\sin (2^{2})}}$

Step 3

Simplify the answer.

Tap for more steps...

Step 3.1

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

$\sqrt{e^{\sin (4)}}$

Step 3.2

Evaluate $\sin (4)$ .

$\sqrt{e^{0.06975647}}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\sqrt{e^{0.06975647}}$

Decimal Form:

$1.03549361 \dots$