Calculus Examples

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

Step 1

Move the term $2$ outside of the limit because it is constant with respect to $n$ .

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

Step 2

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

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

Step 3

Move the limit inside the logarithm.

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

Step 4

Evaluate the limits by plugging in $8$ for all occurrences of $n$ .

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

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

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

$2 \frac{8}{\ln (8)}$

Step 5

Multiply $2 \frac{8}{\ln (8)}$ .

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Combine $2$ and $\frac{8}{\ln (8)}$ .

$\frac{2 \cdot 8}{\ln (8)}$

Multiply $2$ by $8$ .

$\frac{16}{\ln (8)}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{16}{\ln (8)}$

Decimal Form:

$7.69437355 \dots$