Calculus Examples

$lim_{x \to 5} 3^{x + 1}$

Step 1

Evaluate the limit.

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Step 1.1

Move the limit into the exponent.

$3^{lim_{x \to 5} x + 1}$

Step 1.2

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $5$ .

$3^{lim_{x \to 5} x + lim_{x \to 5} 1}$

Step 1.3

Evaluate the limit of $1$ which is constant as $x$ approaches $5$ .

$3^{lim_{x \to 5} x + 1}$

Step 2

Evaluate the limit of $x$ by plugging in $5$ for $x$ .

$3^{5 + 1}$

Step 3

Simplify the answer.

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Step 3.1

Add $5$ and $1$ .

$3^{6}$

Step 3.2

Raise $3$ to the power of $6$ .

$729$