Calculus Examples

$\frac{lim_{h \to 0} {(4 + h)}^{2 - 16}}{h}$

Step 1

Evaluate the limit.

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Step 1.1

Move the exponent $2 - 16$ from ${(4 + h)}^{2 - 16}$ outside the limit using the Limits Power Rule.

$\frac{{(lim_{h \to 0} 4 + h)}^{2 - 16}}{h}$

Step 1.2

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

$\frac{{(lim_{h \to 0} 4 + lim_{h \to 0} h)}^{2 - 16}}{h}$

Step 1.3

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

$\frac{{(4 + lim_{h \to 0} h)}^{2 - 16}}{h}$

Step 2

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

$\frac{{(4 + 0)}^{2 - 16}}{h}$

Step 3

Simplify the answer.

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Step 3.1

Move ${(4 + 0)}^{2 - 16}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{h {(4 + 0)}^{- (2 - 16)}}$

Step 3.2

Simplify the denominator.

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Step 3.2.1

Add $4$ and $0$ .

$\frac{1}{h \cdot 4^{- (2 - 16)}}$

Step 3.2.2

Subtract $16$ from $2$ .

$\frac{1}{h \cdot 4^{- - 14}}$

Step 3.2.3

Multiply $- 1$ by $- 14$ .

$\frac{1}{h \cdot 4^{14}}$

Step 3.2.4

Raise $4$ to the power of $14$ .

$\frac{1}{h \cdot 268435456}$

Step 3.3

Move $268435456$ to the left of $h$ .

$\frac{1}{268435456 h}$