Calculus Examples

$lim_{x \to 7^{+}} \frac{3}{x - 7} - \ln (x - 7)$

Step 1

Combine terms.

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Step 1.1

To write $- \ln (x - 7)$ as a fraction with a common denominator, multiply by $\frac{x - 7}{x - 7}$ .

$lim_{x \to 7^{+}} \frac{3}{x - 7} - \ln (x - 7) \cdot \frac{x - 7}{x - 7}$

Step 1.2

Combine $- \ln (x - 7)$ and $\frac{x - 7}{x - 7}$ .

$lim_{x \to 7^{+}} \frac{3}{x - 7} + \frac{- \ln (x - 7) (x - 7)}{x - 7}$

Step 1.3

Combine the numerators over the common denominator.

$lim_{x \to 7^{+}} \frac{3 - \ln (x - 7) (x - 7)}{x - 7}$

Step 2

Since the numerator is positive and the denominator $x - 7$ approaches zero and is greater than zero for $x$ near $7$ to the right, the function increases without bound.

$\infty$