Precalculus Examples

$\frac{lim_{x \to 0} {(x + 4)}^{4} - 256}{x}$

Step 1

Evaluate the limit.

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Step 1.1

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $0$ .

$\frac{lim_{x \to 0} {(x + 4)}^{4} - lim_{x \to 0} 256}{x}$

Step 1.2

Move the exponent $4$ from ${(x + 4)}^{4}$ outside the limit using the Limits Power Rule.

$\frac{{(lim_{x \to 0} x + 4)}^{4} - lim_{x \to 0} 256}{x}$

Step 1.3

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $0$ .

$\frac{{(lim_{x \to 0} x + lim_{x \to 0} 4)}^{4} - lim_{x \to 0} 256}{x}$

Step 1.4

Evaluate the limit of $4$ which is constant as $x$ approaches $0$ .

$\frac{{(lim_{x \to 0} x + 4)}^{4} - lim_{x \to 0} 256}{x}$

Step 1.5

Evaluate the limit of $256$ which is constant as $x$ approaches $0$ .

$\frac{{(lim_{x \to 0} x + 4)}^{4} - 1 \cdot 256}{x}$

Step 2

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

$\frac{{(0 + 4)}^{4} - 1 \cdot 256}{x}$

Step 3

Simplify the answer.

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Step 3.1

Simplify the numerator.

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Step 3.1.1

Add $0$ and $4$ .

$\frac{4^{4} - 1 \cdot 256}{x}$

Step 3.1.2

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

$\frac{256 - 1 \cdot 256}{x}$

Step 3.1.3

Multiply $- 1$ by $256$ .

$\frac{256 - 256}{x}$

Step 3.1.4

Subtract $256$ from $256$ .

$\frac{0}{x}$

Step 3.2

Divide $0$ by $x$ .

$0$