Calculus Examples

$\frac{lim_{h \to 0} h^{2} + 8 h + 87 - 15}{h}$

Step 1

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

$\frac{lim_{h \to 0} h^{2} + lim_{h \to 0} 8 h + lim_{h \to 0} 87 - lim_{h \to 0} 15}{h}$

Step 2

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

$\frac{{(lim_{h \to 0} h)}^{2} + lim_{h \to 0} 8 h + lim_{h \to 0} 87 - lim_{h \to 0} 15}{h}$

Step 3

Move the term $8$ outside of the limit because it is constant with respect to $h$ .

$\frac{{(lim_{h \to 0} h)}^{2} + 8 lim_{h \to 0} h + lim_{h \to 0} 87 - lim_{h \to 0} 15}{h}$

Step 4

Evaluate the limit of $87$ which is constant as $h$ approaches $0$ .

$\frac{{(lim_{h \to 0} h)}^{2} + 8 lim_{h \to 0} h + 87 - lim_{h \to 0} 15}{h}$

Step 5

Evaluate the limit of $15$ which is constant as $h$ approaches $0$ .

$\frac{{(lim_{h \to 0} h)}^{2} + 8 lim_{h \to 0} h + 87 - 1 \cdot 15}{h}$

Step 6

Evaluate the limits by plugging in $0$ for all occurrences of $h$ .

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Step 6.1

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

$\frac{0^{2} + 8 lim_{h \to 0} h + 87 - 1 \cdot 15}{h}$

Step 6.2

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

$\frac{0^{2} + 8 \cdot 0 + 87 - 1 \cdot 15}{h}$

Step 7

Simplify the numerator.

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Step 7.1

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

$\frac{0 + 8 \cdot 0 + 87 - 1 \cdot 15}{h}$

Step 7.2

Multiply $8$ by $0$ .

$\frac{0 + 0 + 87 - 1 \cdot 15}{h}$

Step 7.3

Multiply $- 1$ by $15$ .

$\frac{0 + 0 + 87 - 15}{h}$

Step 7.4

Add $0$ and $0$ .

$\frac{0 + 87 - 15}{h}$

Step 7.5

Add $0$ and $87$ .

$\frac{87 - 15}{h}$

Step 7.6

Subtract $15$ from $87$ .

$\frac{72}{h}$