Calculus Examples

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

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 $x$ .

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

Step 1.2

Move the limit into the exponent.

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

Step 1.3

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

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

Step 2

Evaluate the limit of $x$ by plugging in $1$ for $x$ .

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

Step 3

Multiply $\frac{1}{2}$ by $1$ .

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

Step 4

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$3.29744254 \dots$