Calculus Examples

$lim_{x \to 0^{+}} e^{2 x}$

Step 1

Evaluate the limit.

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Step 1.1

Move the limit into the exponent.

$e^{lim_{x \to 0^{+}} 2 x}$

Step 1.2

Move the term $2$ outside of the limit because it is constant with respect to $x$ .

$e^{2 lim_{x \to 0^{+}} x}$

Step 2

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

$e^{2 \cdot 0}$

Step 3

Simplify the answer.

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Step 3.1

Multiply $2$ by $0$ .

$e^{0}$

Step 3.2

Anything raised to $0$ is $1$ .

$1$