Calculus Examples

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

Step 1

Split the limit using the Limits Quotient Rule on the limit as $n$ approaches $p^{8}$ .

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

Step 2

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

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

Step 3

Move the limit inside the logarithm.

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

Step 4

Evaluate the limits by plugging in $p^{8}$ for all occurrences of $n$ .

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Step 4.1

Evaluate the limit of $n$ by plugging in $p^{8}$ for $n$ .

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

Step 4.2

Evaluate the limit of $n$ by plugging in $p^{8}$ for $n$ .

$\frac{{(p^{8})}^{2}}{\log_{2} (p^{8})}$

Step 5

Multiply the exponents in ${(p^{8})}^{2}$ .

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Step 5.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{p^{8 \cdot 2}}{\log_{2} (p^{8})}$

Step 5.2

Multiply $8$ by $2$ .

$\frac{p^{16}}{\log_{2} (p^{8})}$