Calculus Examples

$\frac{lim_{n \to 8} {(l g n)}^{901}}{n^{900}}$

Step 1

Evaluate the limit.

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Step 1.1

Move the exponent $901$ from ${(l g n)}^{901}$ outside the limit using the Limits Power Rule.

$\frac{{(lim_{n \to 8} l g n)}^{901}}{n^{900}}$

Step 1.2

Move the term $l g$ outside of the limit because it is constant with respect to $n$ .

$\frac{{(l g lim_{n \to 8} n)}^{901}}{n^{900}}$

Step 2

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

$\frac{{(l g \cdot 8)}^{901}}{n^{900}}$

Step 3

Simplify the answer.

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Step 3.1

Simplify the numerator.

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Step 3.1.1

Apply the product rule to $l g \cdot 8$ .

$\frac{{(l g)}^{901} \cdot 8^{901}}{n^{900}}$

Step 3.1.2

Apply the product rule to $l g$ .

$\frac{l^{901} g^{901} \cdot 8^{901}}{n^{900}}$

Step 3.2

Reorder factors in $\frac{l^{901} g^{901} \cdot 8^{901}}{n^{900}}$ .

$\frac{8^{901} l^{901} g^{901}}{n^{900}}$