Calculus Examples

$lim_{x \to \infty} 4 \log_{3} (2 x + 1) - 5$

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

$lim_{x \to \infty} 4 \log_{3} (2 x + 1) - lim_{x \to \infty} 5$

Since the function $\log_{3} (2 x + 1)$ approaches $\infty$ , the positive constant $4$ times the function also approaches $\infty$ .

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Consider the limit with the constant multiple $4$ removed.

$lim_{x \to \infty} \log_{3} (2 x + 1) - lim_{x \to \infty} 5$

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

$\infty - lim_{x \to \infty} 5$

Evaluate the limit.

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Evaluate the limit of $5$ which is constant as $x$ approaches $\infty$ .

$\infty - 1 \cdot 5$

Simplify the answer.

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Multiply $- 1$ by $5$ .

$\infty - 5$

Infinity plus or minus a number is infinity.

$\infty$