Calculus Examples

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

Step 1

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

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

Step 2

Move the limit inside the logarithm.

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

Step 3

Move the limit inside the logarithm.

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

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 $x$ .

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

Step 4.2

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

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

Step 5

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$0.09151242 \dots$