Chapter 1: Q. 19 (page 153)

Consider the limit expression
$\lim_{x \to \infty} \frac{(2 x - 1) (x^{2} + 1)}{x^{2} - 4}$
Calculate the limit.

Short Answer

Expert verified

The limit of the expression is $\infty$ .

Step by step solution

Step 1. Given

The given expression is

$\lim_{x \to \infty} \frac{(2 x - 1) (x^{2} + 1)}{x^{2} - 4}$

Step 2. Calculation

The evaluated expression is

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

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Consider the limit expression
$\lim_{x \to \infty} \frac{(2 x - 1) (x^{2} + 1)}{x^{2} - 4}$
Calculate the limit.

Short Answer

Step by step solution

Step 1. Given

Step 2. Calculation

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Step by step solution

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One App. One Place for Learning.

Most popular questions from this chapter

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Consider the limit expression
$\lim_{x \to \infty} \frac{(2 x - 1) (x^{2} + 1)}{x^{2} - 4}$
Calculate the limit.