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Chapter 1: Q. 14 (page 153)

Consider the limit expression
$\lim_{x \to 0^{+}} \frac{\sqrt{x} - x^{3}}{x^{2}}$
Calculate the limit.

Short Answer

Expert verified

The limit of the expression is $\infty$ .

Step by step solution

01

Step 1. Given

The given expression is $\lim_{x \to 0^{+}} \frac{\sqrt{x} - x^{3}}{x^{2}}$ .

02

Step 2. Calculation

The evaluated expression is $\lim_{x \to 0^{+}} \frac{\sqrt{x} - x^{3}}{x^{2}} \lim_{x \to 0^{+}} \frac{x^{2} (x^{- \frac{3}{2}} - x)}{x^{2}} = \lim_{x \to 0^{+}} (x^{- \frac{3}{2}} - x) = 0^{- \frac{3}{2}} - 0 = \frac{1}{0} = \infty$

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Most popular questions from this chapter

What are punctured intervals, and why do we need to use them when discussing limits?

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