Calculus Examples

$\frac{lim_{n \to 8} l g (n^{2} + 2 n + 3)}{2 \ln (n)}$

Step 1

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

$\frac{l lim_{n \to 8} g (n^{2} + 2 n + 3)}{2 \ln (n)}$

Step 2

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

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Step 2.1

Evaluate the limit of $g (n^{2} + 2 n + 3)$ by plugging in $8$ for $n$ .

$\frac{l g (8^{2} + 2 \cdot 8 + 3)}{2 \ln (n)}$

Step 2.2

Simplify each term.

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Step 2.2.1

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

$\frac{l g (64 + 2 \cdot 8 + 3)}{2 \ln (n)}$

Step 2.2.2

Multiply $2$ by $8$ .

$\frac{l g (64 + 16 + 3)}{2 \ln (n)}$

Step 2.3

Add $64$ and $16$ .

$\frac{l g (80 + 3)}{2 \ln (n)}$

Step 2.4

Add $80$ and $3$ .

$\frac{l g (83)}{2 \ln (n)}$