Calculus Examples

$lim_{x \to 2} 4^{3 x - 1}$

Step 1

Evaluate the limit.

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Step 1.1

Move the limit into the exponent.

$4^{lim_{x \to 2} 3 x - 1}$

Step 1.2

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $2$ .

$4^{lim_{x \to 2} 3 x - lim_{x \to 2} 1}$

Step 1.3

Move the term $3$ outside of the limit because it is constant with respect to $x$ .

$4^{3 lim_{x \to 2} x - lim_{x \to 2} 1}$

Step 1.4

Evaluate the limit of $1$ which is constant as $x$ approaches $2$ .

$4^{3 lim_{x \to 2} x - 1 \cdot 1}$

Step 2

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

$4^{3 \cdot 2 - 1 \cdot 1}$

Step 3

Simplify the answer.

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Step 3.1

Simplify each term.

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Step 3.1.1

Multiply $3$ by $2$ .

$4^{6 - 1 \cdot 1}$

Step 3.1.2

Multiply $- 1$ by $1$ .

$4^{6 - 1}$

Step 3.2

Subtract $1$ from $6$ .

$4^{5}$

Step 3.3

Raise $4$ to the power of $5$ .

$1024$