Calculus Examples

$lim_{n \to 8} \frac{1}{n^{2}}$

Step 1

Evaluate the limit.

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Step 1.1

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

$\frac{lim_{n \to 8} 1}{lim_{n \to 8} n^{2}}$

Step 1.2

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

$\frac{1}{lim_{n \to 8} n^{2}}$

Step 1.3

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

$\frac{1}{{(lim_{n \to 8} n)}^{2}}$

Step 2

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

$\frac{1}{8^{2}}$

Step 3

Raise $8$ to the power of $2$ .

$\frac{1}{64}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{64}$

Decimal Form:

$0.015625$