Chapter 1: Q. 50 (page 149)

Calculate each limit in Exercises 35–80.
$\lim_{x \to - \infty} \frac{1 - 2 x^{2}}{(3 - x) (3 + 4 x)}$

Short Answer

Expert verified

The limit is $\frac{1}{2}$

Step by step solution

Step 1. Given Information:

Given expression: $\lim_{x \to - \infty} \frac{1 - 2 x^{2}}{(3 - x) (3 + 4 x)}$

We want to find limit of given expression.

Step 2. Solution:

Simplify the denominator we get

$\lim_{x \to - \infty} \frac{1 - 2 x^{2}}{(3 - x) (3 + 4 x)} = \lim_{x \to - \infty} \frac{1 - 2 x^{2}}{9 + 9 x - 4 x^{2}}$

Now take x² common form numerator and denominator and simplify we get

role="math" localid="1648190481005" $\lim_{x \to - \infty} \frac{1 - 2 x^{2}}{9 + 9 x - 4 x^{2}} = \lim_{x \to - \infty} \frac{x^{2} (\frac{1}{x^{2}} - 2)}{x^{2} (\frac{9}{x^{2}} + \frac{9}{x} - 4)} = \lim_{x \to - \infty} \frac{\frac{1}{x^{2}} - 2}{\frac{9}{x^{2}} + \frac{9}{x} - 4}$

Now take limit we get

$\lim_{x \to - \infty} \frac{\frac{1}{- \infty^{2}} - 2}{\frac{9}{- \infty^{2}} + \frac{9}{\infty} - 4} = \lim_{x \to - \infty} \frac{- 2}{- 4} = \lim_{x \to - \infty} \frac{4}{2} = \frac{1}{2}$

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Calculate each limit in Exercises 35–80.
$\lim_{x \to - \infty} \frac{1 - 2 x^{2}}{(3 - x) (3 + 4 x)}$

Short Answer

Step by step solution

Step 1. Given Information:

Step 2. Solution:

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Calculate each limit in Exercises 35–80.limx→-∞1-2x2(3-x)(3+4x)

Short Answer

Step by step solution

Step 1. Given Information:

Step 2. Solution:

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Mechanics Maths

Decision Maths

Theoretical and Mathematical Physics

Discrete Mathematics

Statistics

Study anywhere. Anytime. Across all devices.

Calculate each limit in Exercises 35–80.
$\lim_{x \to - \infty} \frac{1 - 2 x^{2}}{(3 - x) (3 + 4 x)}$