Calculus Examples

$lim_{x \to 8} \frac{4 \ln (x)}{x}$

Step 1

Move the term $4$ outside of the limit because it is constant with respect to $x$ .

$4 lim_{x \to 8} \frac{\ln (x)}{x}$

Step 2

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

$4 \frac{lim_{x \to 8} \ln (x)}{lim_{x \to 8} x}$

Step 3

Move the limit inside the logarithm.

$4 \frac{\ln (lim_{x \to 8} x)}{lim_{x \to 8} x}$

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 $x$ .

$4 \frac{\ln (8)}{lim_{x \to 8} x}$

Step 4.2

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

$4 \frac{\ln (8)}{8}$

Step 5

Cancel the common factor of $4$ .

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Step 5.1

Factor $4$ out of $8$ .

$4 \frac{\ln (8)}{4 (2)}$

Step 5.2

Cancel the common factor.

$4 \frac{\ln (8)}{4 \cdot 2}$

Step 5.3

Rewrite the expression.

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

Step 6

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$1.03972077 \dots$