Calculus Examples

$lim_{x \to \infty} - \ln (3 x) - 2$

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

$- lim_{x \to \infty} \ln (3 x) - lim_{x \to \infty} 2$

As log approaches infinity, the value goes to $\infty$ .

$- \infty - lim_{x \to \infty} 2$

Evaluate the limit.

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Evaluate the limit of $2$ which is constant as $x$ approaches $\infty$ .

$- \infty - 1 \cdot 2$

Simplify the answer.

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Simplify each term.

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A non-zero constant times infinity is infinity.

$- \infty - 1 \cdot 2$

Multiply $- 1$ by $2$ .

$- \infty - 2$

Infinity plus or minus a number is infinity.

$- \infty$