Calculus Examples

$lim_{x \to 8} \frac{1}{x^{3}}$

Step 1

Evaluate the limit.

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Step 1.1

Split the limit using the Limits Quotient Rule on the limit as $x$ approaches $8$ .

$\frac{lim_{x \to 8} 1}{lim_{x \to 8} x^{3}}$

Step 1.2

Evaluate the limit of $1$ which is constant as $x$ approaches $8$ .

$\frac{1}{lim_{x \to 8} x^{3}}$

Step 1.3

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

$\frac{1}{{(lim_{x \to 8} x)}^{3}}$

Step 2

Evaluate the limit of $x$ by plugging in $8$ for $x$ .

$\frac{1}{8^{3}}$

Step 3

Raise $8$ to the power of $3$ .

$\frac{1}{512}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{512}$

Decimal Form:

$0.00195312 \dots$