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Chapter 1: Q. 54 (page 149)

Calculate each limit in Exercises 35–80.
$\underset{x \to 0^{+}}{l i m} \frac{x^{- 3}}{x^{2} - x^{- 1}}$

Short Answer

Expert verified

The limit is infinity.

Step by step solution

01

Step 1. Given information

The given expression is $\underset{x \to 0^{+}}{l i m} \frac{x^{- 3}}{x^{2} - x^{- 1}}$

02

Step 2. Calculation

The limit is calculated as below,

\underset{x \to 0^{+}}{l i m} \frac{x^{- 3}}{x^{2} - x^{- 1}} = \underset{x \to 0^{+}}{l i m} \frac{\frac{1}{x^{3}}}{x^{2} - \frac{1}{x}} = \underset{x \to 0^{+}}{l i m} \frac{\frac{1}{x^{3}}}{\frac{x^{3} - 1}{x}} = \underset{x \to 0^{+}}{l i m} \frac{1}{x^{2} (x^{3} - 1)} = \frac{1}{0^{2} (0^{3} - 1)} = \infty

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Most popular questions from this chapter

Sketch a labeled graph of a function that satisfies the hypothesis of the Extreme Value Theorem, and illustrate on your graph that the conclusion of the Extreme Value Theorem follows.

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