Calculus Examples

$lim_{x \to 0^{-}} 17 + \frac{2}{x^{3}}$

Step 1

Evaluate the limit.

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Step 1.1

Split the limit using the Sum of Limits Rule on the limit as $x$ approaches $0$ .

$lim_{x \to 0^{-}} 17 + lim_{x \to 0^{-}} \frac{2}{x^{3}}$

Step 1.2

Evaluate the limit of $17$ which is constant as $x$ approaches $0$ .

$17 + lim_{x \to 0^{-}} \frac{2}{x^{3}}$

Step 2

Since the numerator is a constant and the denominator approaches $0$ when $x$ approaches $0$ from the left, the fraction $\frac{2}{x^{3}}$ approaches negative infinity.

$17 + - \infty$

Step 3

Infinity plus or minus a number is infinity.

$- \infty$