Calculus Examples

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

Step 1

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

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

Step 2

Move the limit inside the logarithm.

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

Step 3

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

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Step 3.1

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

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

Step 3.2

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

$\frac{8 + \ln (8)}{n^{2} + 1}$