Calculus Examples

$\frac{lim_{h \to 0} (- 8 + h^{2}) (- 64)}{h}$

Step 1

Evaluate the limit.

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Step 1.1

Move the term $- 64$ outside of the limit because it is constant with respect to $h$ .

$\frac{- 64 lim_{h \to 0} - 8 + h^{2}}{h}$

Step 1.2

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

$\frac{- 64 (- lim_{h \to 0} 8 + lim_{h \to 0} h^{2})}{h}$

Step 1.3

Evaluate the limit of $8$ which is constant as $h$ approaches $0$ .

$\frac{- 64 (- 1 \cdot 8 + lim_{h \to 0} h^{2})}{h}$

Step 1.4

Move the exponent $2$ from $h^{2}$ outside the limit using the Limits Power Rule.

$\frac{- 64 (- 8 + {(lim_{h \to 0} h)}^{2})}{h}$

Step 2

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

$\frac{- 64 (- 8 + 0^{2})}{h}$

Step 3

Simplify the answer.

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Step 3.1

Simplify the numerator.

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Step 3.1.1

Raising $0$ to any positive power yields $0$ .

$\frac{- 64 (- 8 + 0)}{h}$

Step 3.1.2

Add $- 8$ and $0$ .

$\frac{- 64 \cdot - 8}{h}$

Step 3.2

Multiply $- 64$ by $- 8$ .

$\frac{512}{h}$