Calculus Examples

$lim_{x \to - 2} e^{\frac{x^{2}}{2}}$

Step 1

Evaluate the limit.

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Step 1.1

Move the limit into the exponent.

$e^{lim_{x \to - 2} \frac{x^{2}}{2}}$

Step 1.2

Move the term $\frac{1}{2}$ outside of the limit because it is constant with respect to $x$ .

$e^{\frac{1}{2} lim_{x \to - 2} x^{2}}$

Step 1.3

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

$e^{\frac{1}{2} {(lim_{x \to - 2} x)}^{2}}$

Step 2

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

$e^{\frac{1}{2} {(- 2)}^{2}}$

Step 3

Simplify the answer.

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Step 3.1

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

$e^{\frac{1}{2} \cdot 4}$

Step 3.2

Cancel the common factor of $2$ .

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Step 3.2.1

Factor $2$ out of $4$ .

$e^{\frac{1}{2} \cdot (2 (2))}$

Step 3.2.2

Cancel the common factor.

$e^{\frac{1}{2} \cdot (2 \cdot 2)}$

Step 3.2.3

Rewrite the expression.

$e^{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$e^{2}$

Decimal Form:

$7.38905609 \dots$