/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 47 Use a graphing utility to graph ... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 47

Use a graphing utility to graph the function. Use the graph to determine any \(x\) -values at which the function is not continuous. $$ f(x)=\llbracket x \rrbracket-x $$

Short Answer

Expert verified
The function \(f(x) = \llbracket x \rrbracket - x\) is not continuous at the integer values of \(x\).

Step by step solution

01

Define the function

The given function is \(f(x) = \llbracket x \rrbracket - x\). Here, \(\llbracket x \rrbracket\) is the floor function of \(x\), which returns the largest integer less than or equal to \(x\).
02

Plot the function

Now, plot the function using a graphing utility. The graph will be a downward slant for each integer interval with slope -1. Each segment will start at a given integer and reach to just before the next.
03

Identify discontinuities

The points of discontinuity are where the function jumps. These are the integer values, as the floor function rounds down to the next lowest integer. So, at every integer \(x\), the function is not continuous.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Verify each identity (a) \(\arcsin (-x)=-\arcsin x, \quad|x| \leq 1\) (b) \(\arccos (-x)=\pi-\arccos x, \quad|x| \leq 1\)

Describe the difference between a discontinuity that is removable and one that is nonremovable. In your explanation, give examples of the following. (a) A function with a nonremovable discontinuity at \(x=2\) (b) A function with a removable discontinuity at \(x=-2\) (c) A function that has both of the characteristics described in parts (a) and (b)

True or False? Determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. If \(f(x)=g(x)\) for \(x \neq c\) and \(f(c) \neq g(c),\) then either \(f\) or \(g\) is not continuous at \(c\).

In Exercises \(25-34,\) find the limit. $$ \lim _{x \rightarrow 0^{-}}\left(x^{2}-\frac{2}{x}\right) $$

Write the expression in algebraic form. \(\cos \left(\arcsin \frac{x-h}{r}\right)\)
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Probability and Statistics

Read Explanation

Pure Maths

Read Explanation

Logic and Functions

Read Explanation

Mechanics Maths

Read Explanation

Calculus

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.