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Chapter 1: Q 10. (page 107)

Write each of the inequalities in interval notation:
$|(3 x + 1) - 2| < 0.1$

Short Answer

Expert verified

Solution is $(0.3, 0.3666 . . .)$

Step by step solution

01

Step 1. Given information

An inequality is $|(3 x + 1) - 2| < 0.1$

02

Step 2. Solution of the inequality.

$\begin{array}{rcl} |(3 x + 1) - 2| & < & 0.1 \\ - 0.1 & < & (3 x + 1) - 2 < 0.1 \end{array}$

$x > 0.3$ and $x < 0.3666 . . .$

So, solution is $(0.3, 0.3666 . . .)$

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Most popular questions from this chapter

Use the delta-epsilon definition of continuity to argue that f is or is not continuous at the indicated point $x = c$ .

$f (x) = \{\begin{aligned} 2 - x, if x rational \\ x^{2}, if x irrational, \end{aligned} c = 1$

Write each of the inequalities in interval notation:

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

$\lim_{x \to 1} \frac{1 - \cos (x - 1)}{x}$

For each functionf graphed in Exercises23–26, describe the intervals on whichf is continuous. For each discontinuity off, describe the type of discontinuity and any one-sided continuity. Justify your answers about discontinuities with limit statements.

State what it means for a functionf to be continuous at a point x = c, in terms of the delta–epsilon definition of limit.

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