Chapter 1: Q. 51 (page 149)

Calculate each limit in Exercises
$\lim_{x \to 0^{+}} (x^{- \frac{1}{3}} - x^{- \frac{1}{2}})$

Short Answer

Expert verified

The value of $\lim_{x \to 0^{+}} (x^{- \frac{1}{3}} - x^{- \frac{1}{2}})$ is $- \infty .$

Step by step solution

Step 1. Given information

The given limit is $\lim_{x \to 0^{+}} (x^{- \frac{1}{3}} - x^{- \frac{1}{2}}) .$

Step 2. value of the expression.

Evaluate the expression.

$\lim_{x \to 0^{+}} (x^{- \frac{1}{3}} - x^{- \frac{1}{2}}) = \lim_{x \to 0^{+}} (\frac{1}{x^{\frac{1}{3}}} - \frac{1}{x^{\frac{1}{2}}}) = \lim_{x \to 0^{+}} (\frac{1}{\sqrt[3]{x}} - \frac{1}{\sqrt{x}}) = \frac{1}{\sqrt[3]{0}} - \frac{1}{\sqrt{0}} = \infty - \infty = - \infty$

The value of limit is $- \infty .$

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Calculate each limit in Exercises
$\lim_{x \to 0^{+}} (x^{- \frac{1}{3}} - x^{- \frac{1}{2}})$

Short Answer

Step by step solution

Step 1. Given information

Step 2. value of the expression.

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Calculate each limit in Exercises
$\lim_{x \to 0^{+}} (x^{- \frac{1}{3}} - x^{- \frac{1}{2}})$