Chapter 14: Q. 42 (page 889)

In Problems 33– 44, find the one-sided limit.
$\lim_{x \to 0^{+}} \frac{x^{3} - x^{2}}{x^{4} + x^{2}}$

Short Answer

Expert verified

the limit value

$\lim_{x \to 0^{+}} \frac{x^{3} - x^{2}}{x^{4} + x^{2}} = - 1$

Step by step solution

step 1.introduction

given limit

$\lim_{x \to 0^{+}} \frac{x^{3} - x^{2}}{x^{4} + x^{2}}$

step 2.equation simplification

consider the equation

$\frac{x^{3} - x^{2}}{x^{4} + x^{2}} = \frac{x^{2} (x - 1)}{x^{2} (x^{2} + 1)} = \frac{x - 1}{x^{2} + 1}$

step 3.the solution

the limit values

$\frac{x^{3} - x^{2}}{x^{4} + x^{2}} = \lim_{x \to 0^{+}} \frac{x - 1}{x^{2} + 1} = \frac{0 - 1}{0 + 1} = - 1$

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In Problems 33– 44, find the one-sided limit.
$\lim_{x \to 0^{+}} \frac{x^{3} - x^{2}}{x^{4} + x^{2}}$

Short Answer

Step by step solution

step 1.introduction

step 2.equation simplification

step 3.the solution

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In Problems 33– 44, find the one-sided limit.limx→0+x3-x2x4+x2

Short Answer

Step by step solution

step 1.introduction

step 2.equation simplification

step 3.the solution

One App. One Place for Learning.

Most popular questions from this chapter

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Study anywhere. Anytime. Across all devices.

In Problems 33– 44, find the one-sided limit.
$\lim_{x \to 0^{+}} \frac{x^{3} - x^{2}}{x^{4} + x^{2}}$