Calculus Examples

$lim_{x \to 0^{-}} - 14 - \frac{11}{x^{4}}$

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 $0$ .

$- lim_{x \to 0^{-}} 14 - lim_{x \to 0^{-}} \frac{11}{x^{4}}$

Step 1.2

Evaluate the limit of $14$ which is constant as $x$ approaches $0$ .

$- 1 \cdot 14 - lim_{x \to 0^{-}} \frac{11}{x^{4}}$

Step 2

Since the numerator is a constant and the denominator approaches $0$ when $x$ approaches $0$ from the left, the fraction $\frac{11}{x^{4}}$ approaches infinity.

$- 14 - \infty$

Step 3

Simplify the answer.

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Step 3.1

A non-zero constant times infinity is infinity.

$- 14 + - \infty$

Step 3.2

Infinity plus or minus a number is infinity.

$- \infty$