Calculus Examples

$lim_{x \to 0^{+}} x - \frac{1}{x^{3}}$

Step 1

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

$lim_{x \to 0^{+}} x - lim_{x \to 0^{+}} \frac{1}{x^{3}}$

Step 2

Since the numerator is a constant and the denominator approaches $0$ when $x$ approaches $0$ from the right, the fraction $\frac{1}{x^{3}}$ approaches infinity.

$lim_{x \to 0^{+}} x - \infty$

Step 3

Evaluate the limit of $x$ by plugging in $0$ for $x$ .

$0 - \infty$

Step 4

Simplify the answer.

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Step 4.1

A non-zero constant times infinity is infinity.

$0 + - \infty$

Step 4.2

Subtract $\infty$ from $0$ .

$- \infty$