Maclaurin Series Calculator

How to Use the Maclaurin Series Calculator

Step 1: Select a Function

Begin by choosing the mathematical function for which you want to calculate the Maclaurin series. This calculator offers the following predefined functions:

• e^x
• sin(x)
• cos(x)
• ln(1+x)

Select one of these functions from the dropdown menu labeled Select Function.

Step 2: Enter the x Value

After selecting the desired function, move to the x Value input field. Enter the value of x for which you wish to evaluate the series. Note that this calculator restricts the valid range for x between -10 and 10, inclusive. Ensure your input is within this range and adheres to a step size of 0.1 for precision.

Step 3: Define the Number of Terms

Next, you need to specify the extent of the Maclaurin series by determining how many terms (up to a maximum of 10) you wish to include in the calculation. Enter a whole number from 1 to 10 in the Number of Terms field.

Step 4: Review Calculated Terms

Upon submitting your inputs, the calculator will compute and display the first four terms of the series, according to your specified input and function:

• First Term
• Second Term
• Third Term
• Fourth Term

Each term will be calculated using the corresponding formula for the chosen function, with the values rounded to six decimal places for clarity.

Step 5: Analyze the Results

In addition to the individual terms, the calculator will automatically compute and present the Series Sum, which is the sum of the terms you requested. Moreover, the Actual Function Value at the specified x is presented for comparison.

Step 6: Evaluate the Error

The calculator provides the Absolute Error to help assess the accuracy of the Maclaurin series approximation. This error value is calculated as the absolute difference between the actual function value and the series sum. A smaller error suggests a closer approximation to the actual value, which can be valuable for evaluating the sufficiency of the number of terms you selected.