Math Problem Statement

Determine the points in the interval ​(11​,66​) at which the function has a discontinuity. At each point of​ discontinuity, state the conditions in the continuity checklist that are violated. 1.​ f(a) is defined​ (a is in the domain of​ f). 2. ModifyingBelow lim With x right arrow alimx→a ​f(x) exists. 3. ModifyingBelow lim With x right arrow a f left parenthesis x right parenthesis equals f left parenthesis a right parenthesislimx→a f(x)=f(a) ​(the value of f equals the limit of f at​ a).

Solution

To determine the points in the interval (11,66)(11, 66) at which a function has a discontinuity, you need to check for places where one or more of the conditions for continuity are violated. These conditions are:

  1. f(a)f(a) is defined: The function is defined at the point aa (meaning aa is in the domain of the function).
  2. lim⁡x→af(x)\lim_{x \to a} f(x) exists: The limit of the function as xx approaches aa exists.
  3. **( \lim_{x \to a} f(x) = f(a)

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Continuity
Limits
Functions

Formulas

\lim_{x \to a} f(x)
f(a)

Theorems

Continuity at a Point
Limits of Functions

Suitable Grade Level

Grades 11-12

Related Recommendation

Determine Points of Discontinuity in the Interval (1,6) Using the Continuity Checklist

Determine Points of Discontinuity and Violated Conditions in the Interval (1,6)

Determine Continuity of a Function Using a Graph

Determining Discontinuities in a Function on Interval [0,4]

Discontinuity of Piecewise Functions at x = 2