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Chapter 1: Q 7. (page 107)

Write each of the inequalities in interval notation:
$0 < | x - 2 | < 0.1$

Short Answer

Expert verified

Answer is $(1.9, 2) \cup (2, 2.1)$

Step by step solution

01

Step 1. Given information

An inequality is $0 < | x - 2 | < 0.1$

02

Step 2. Explanation

$0 < | x - 2 | < 0.1$

$0 < | x - 2 |$ and $| x - 2 | < 0.1$

( $x < 2$ or $x > 2$ )and $1.9 < x < 2.1$

$1.9 < x < 2$ or width="74">2<x<2.1

So, interval notation is $(1.9, 2) \cup (2, 2.1)$

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Most popular questions from this chapter

Sketch a labeled graph of a function that fails to satisfy the hypothesis of the Intermediate Value Theorem, and illustrate on your graph that the conclusion of the Intermediate Value Theorem does not necessarily hold.

Write each of the inequalities in interval notation:

$|f (x) - L| < \in$

Calculate each of the limits:

$\lim_{x \to 1} x \sin^{- 1} \frac{x}{2}$ .

Write delta-epsilon proofs for each of the limit statements in Exercises $47 - 60 .$

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

Write delta-epsilon proofs for each of the limit statements $\lim_{x \to c} f (x) = L$ in Exercises $47 - 60$ .

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

See all solutions

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