Math Problem Statement

name the disconiutny at x=2

Name the discontinuity at x=2.

Solution

The graph shows a discontinuity at x=2x = 2 with an open circle, indicating a removable discontinuity. A removable discontinuity occurs when the function is not defined at a specific point (as shown by the open circle) but can be made continuous by redefining the function's value at that point.

Let me know if you'd like to dive deeper into discontinuities or have other questions.

Here are 5 related questions to explore:

  1. What are the other types of discontinuities besides removable?
  2. How can a removable discontinuity be "fixed" mathematically?
  3. What are the implications of removable discontinuities in calculus, especially for limits?
  4. How can you determine if a function is continuous from a graph?
  5. What role do discontinuities play in real-world applications of mathematics?

Tip: Always check limits from both sides to confirm the type of discontinuity!

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Math Problem Analysis

Mathematical Concepts

Removable Discontinuity
Continuity
Limits

Formulas

Limit as x approaches c from the left and right

Theorems

Definition of Removable Discontinuity

Suitable Grade Level

Grades 11-12