Calculus Examples

$lim_{x \to 8} 7 x - \ln (x)$

Step 1

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

$lim_{x \to 8} 7 x - lim_{x \to 8} \ln (x)$

Step 2

Move the term $7$ outside of the limit because it is constant with respect to $x$ .

$7 lim_{x \to 8} x - lim_{x \to 8} \ln (x)$

Step 3

Move the limit inside the logarithm.

$7 lim_{x \to 8} x - \ln (lim_{x \to 8} x)$

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 $x$ .

$7 \cdot 8 - \ln (lim_{x \to 8} x)$

Step 4.2

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

$7 \cdot 8 - \ln (8)$

Step 5

Multiply $7$ by $8$ .

$56 - \ln (8)$

Step 6

The result can be shown in multiple forms.

Exact Form:

$56 - \ln (8)$

Decimal Form:

$53.92055845 \dots$