Discontinuity Calculator

How to Use the Discontinuity Calculator

The Discontinuity Calculator is designed to help you analyze different types of discontinuities in functions. Follow the steps below to effectively use this tool.

Step 1: Provide Discontinuity Details

• Select the Type of Discontinuity: From the dropdown menu, choose one of the following options:
  • Removable Discontinuity: A discontinuity that can be “removed” by redefining the function at that point.
  • Jump Discontinuity: A discontinuity where the function has a sudden “jump” at the point.
  • Infinite Discontinuity: A discontinuity where the function approaches infinity around the point.

Step 2: Enter Point of Discontinuity Details

• x-value (Point of Discontinuity): Enter the x-value of the point where you suspect a discontinuity exists.
• Left-hand Limit: Input the value of the function as it approaches the x-value from the left.
• Right-hand Limit: Input the value of the function as it approaches the x-value from the right.
• Function Value at x: Enter the actual value of the function at the x-value you’ve entered.

Step 3: Review the Results

After providing all the necessary inputs, review the results produced by the calculator:

• Is the Function Discontinuous? This field will display a result indicating whether or not a discontinuity exists at the given point.
• Size of Jump (if applicable): If a jump discontinuity is present, this field will display the size of the jump between the left and right limits.
• Does Two-sided Limit Exist? This result informs you if the left and right limits are approximately equal, suggesting that a two-sided limit exists.
• Is Discontinuity Removable? This field will indicate whether the discontinuity can potentially be removed by redefining the function at the given point.

By following these steps, you can efficiently use the Discontinuity Calculator to analyze discontinuities in functions.