Limit Calculator

Guide to Using the Limit Calculator

Step 1: Select the Type of Function

Begin by choosing the type of function for which you want to compute the limit. You have three options available:

• Polynomial Function
• Rational Function
• Exponential Function

This selection is essential and required for the calculator to proceed.

Step 2: Enter the x Value (Approaching)

Input the x value that the function is approaching. This is a crucial input field because it determines the point of evaluation for limits. Ensure that the value you input is precise, using steps of 0.1 for accuracy.

Step 3: Specify the Coefficient

Next, provide the coefficient for the function being evaluated. This value should also be entered with precision, using steps of 0.1 to maintain consistency and accuracy in calculations.

Step 4: Input the Exponent

For functions involving powers, input the exponent value. Since exponents are typically whole numbers, this field has a step size of 1. This input will affect how the limit is calculated.

Step 5: Choose the Direction of Approach

Decide the direction from which the function approaches the x value. The options include:

• Both Sides: Calculate limits from both left and right sides.
• Left Side: Calculate the limit from the left-hand side only.
• Right Side: Calculate the limit from the right-hand side only.

This selection is required and affects how the final limits are computed.

Understanding the Results

Left-hand and Right-hand Limits

The calculator will compute two important values: the Left-hand Limit and the Right-hand Limit. These represent the limit of the function as it approaches the x value from the left and right, respectively. For both limits, a minor increment or decrement of 0.001 is applied to the x value, and the result is formatted to four decimal places.

Determining Limit Existence

The calculator checks whether the limits from both sides are approximately equal. If the absolute difference between them is less than 0.0001, the limit is considered to exist, and the result will indicate ‘Yes’. Otherwise, it will show ‘No’.

Calculating the Limit Value

If the limit exists, the calculator provides the Limit Value using the given x value, coefficient, and exponent, formatted to four decimal places. If the limit does not exist, it displays ‘DNE’ (Does Not Exist).