Calculus Examples

$lim_{x \to - 3} 5 e^{x + 3}$

Step 1

Evaluate the limit.

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Step 1.1

Move the term $5$ outside of the limit because it is constant with respect to $x$ .

$5 lim_{x \to - 3} e^{x + 3}$

Step 1.2

Move the limit into the exponent.

$5 e^{lim_{x \to - 3} x + 3}$

Step 1.3

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $- 3$ .

$5 e^{lim_{x \to - 3} x + lim_{x \to - 3} 3}$

Step 1.4

Evaluate the limit of $3$ which is constant as $x$ approaches $- 3$ .

$5 e^{lim_{x \to - 3} x + 3}$

Step 2

Evaluate the limit of $x$ by plugging in $- 3$ for $x$ .

$5 e^{- 3 + 3}$

Step 3

Simplify the answer.

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Step 3.1

Add $- 3$ and $3$ .

$5 e^{0}$

Step 3.2

Anything raised to $0$ is $1$ .

$5 \cdot 1$

Step 3.3

Multiply $5$ by $1$ .

$5$