Chapter 1: Q. 4 (page 107)

Suppose you show that $| (1 - 2 x) - (- 5) | < 0.05$ for all x with $0 < | x - 3 | < 0.025$ Explain why this does not prove thatrole="math" localid="1648055981096" $\underset{x \to 3}{l i m} (1 - 2 x) = - 5$

Short Answer

Expert verified

As $- \frac{ε}{2} < | x - 3 | < δ$ thus we cannot say that $\underset{x \to 3}{l i m} (1 - 2 x) = - 5$

Step by step solution

Step 1. Given Information

The given limit expression is $\underset{x \to 3}{l i m} (1 - 2 x) = - 5$

Step 2. Explanation

From the given limit expression, we have,

$f (x) = 1 - 2 x, c = 3, L = - 5$

Hence, delta-epsilon statement will be as follows,

For all epsilon positive there exists a delta positive if $0 < | x - 3 | < δ$

Then,

$| (1 - 2 x) - (- 5) | < ε | 1 - 2 x + 5 | < ε | 6 - 2 x | < ε - 2 | x - 3 | < ε | x - 3 | > - \frac{ε}{2}$

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Suppose you show that $| (1 - 2 x) - (- 5) | < 0.05$ for all x with $0 < | x - 3 | < 0.025$ Explain why this does not prove thatrole="math" localid="1648055981096" $\underset{x \to 3}{l i m} (1 - 2 x) = - 5$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Explanation

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Suppose you show that |(1-2x)-(-5)|<0.05 for all x with 0<|x-3|<0.025Explain why this does not prove thatrole="math" localid="1648055981096" limx→3(1-2x)=-5

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Explanation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Discrete Mathematics

Statistics

Calculus

Probability and Statistics

Pure Maths

Study anywhere. Anytime. Across all devices.

Suppose you show that $| (1 - 2 x) - (- 5) | < 0.05$ for all x with $0 < | x - 3 | < 0.025$ Explain why this does not prove thatrole="math" localid="1648055981096" $\underset{x \to 3}{l i m} (1 - 2 x) = - 5$