Calculus Examples

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

Step 1

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

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

Step 2

Move the limit inside the logarithm.

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

Step 3

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

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

Step 4

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

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Step 4.1

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

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

Step 4.2

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

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

Step 5

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

$\frac{\ln (8)}{64}$