Calculus Examples

$\frac{lim_{h \to 7} h^{3} - 343}{h - 7}$

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 $h$ approaches $7$ .

$\frac{lim_{h \to 7} h^{3} - lim_{h \to 7} 343}{h - 7}$

Step 1.2

Move the exponent $3$ from $h^{3}$ outside the limit using the Limits Power Rule.

$\frac{{(lim_{h \to 7} h)}^{3} - lim_{h \to 7} 343}{h - 7}$

Step 1.3

Evaluate the limit of $343$ which is constant as $h$ approaches $7$ .

$\frac{{(lim_{h \to 7} h)}^{3} - 1 \cdot 343}{h - 7}$

Step 2

Evaluate the limit of $h$ by plugging in $7$ for $h$ .

$\frac{7^{3} - 1 \cdot 343}{h - 7}$

Step 3

Simplify the answer.

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Step 3.1

Simplify the numerator.

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Step 3.1.1

Raise $7$ to the power of $3$ .

$\frac{343 - 1 \cdot 343}{h - 7}$

Step 3.1.2

Multiply $- 1$ by $343$ .

$\frac{343 - 343}{h - 7}$

Step 3.1.3

Subtract $343$ from $343$ .

$\frac{0}{h - 7}$

Step 3.2

Divide $0$ by $h - 7$ .

$0$