Chapter 3: Q. 25 (page 314)

L’Hˆopital’s Rule limit calculations: Calculate each of the
limits that follow. Some of these limits are easier to calculate
by using L’Hopital’s rule, and some are not.
$\lim_{x \to \infty} \frac{x^{- 2}}{x^{- 3} + 1}$

Short Answer

Expert verified

Value of limit is zero and it is easy to find without L'Hospitals rule

Step by step solution

Step 1. Given information

An expression is given as $\lim_{x \to \infty} \frac{x^{- 2}}{x^{- 3} + 1}$

Step 2. Evaluating limit

Simplify by using properties as,

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

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L’Hˆopital’s Rule limit calculations: Calculate each of the
limits that follow. Some of these limits are easier to calculate
by using L’Hopital’s rule, and some are not.
$\lim_{x \to \infty} \frac{x^{- 2}}{x^{- 3} + 1}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Evaluating limit

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L’Hˆopital’s Rule limit calculations: Calculate each of thelimits that follow. Some of these limits are easier to calculateby using L’Hopital’s rule, and some are not.limx→∞x-2x-3+1

Short Answer

Step by step solution

Step 1. Given information

Step 2. Evaluating limit

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Statistics

Applied Mathematics

Decision Maths

Theoretical and Mathematical Physics

Pure Maths

Study anywhere. Anytime. Across all devices.

L’Hˆopital’s Rule limit calculations: Calculate each of the
limits that follow. Some of these limits are easier to calculate
by using L’Hopital’s rule, and some are not.
$\lim_{x \to \infty} \frac{x^{- 2}}{x^{- 3} + 1}$