Taylor Series Calculator

This Taylor Series Calculator allows users to approximate the value of functions such as e^x, sin(x), cos(x), and ln(1+x) using Taylor series at a specified point and evaluate the approximation’s error with respect to the actual function value.

Use Our Taylor Series Calculator

How to Use the Taylor Series Calculator

Step 1: Select the Function

Begin by selecting the function for which you want to calculate the Taylor series. The options available are:

  • e^x – Exponential function
  • sin(x) – Sine function
  • cos(x) – Cosine function
  • ln(1+x) – Natural logarithm function of (1+x)

This selection is mandatory, so be sure to pick one that aligns with your needs.

Step 2: Enter the x Value

In the next input field, enter the x value where you would like to evaluate the Taylor Series. This value should be between -10 and 10.

This field is essential for the calculation, so a valid number within the given range is required.

Step 3: Set the Center Point

Provide the Center point (a) for the Taylor series expansion. This value also needs to be between -10 and 10.

This point is where the function will be centered, so make sure to enter it accurately.

Step 4: Specify the Number of Terms

Indicate the Number of Terms you wish to use for the Taylor series approximation. The calculator allows a selection between 1 and 10 terms.

The number of terms determines the approximation’s accuracy; more terms generally result in a closer approximation to the actual function.

Reading the Results

Upon entering all the necessary inputs, the calculator will display the following results:

  • Taylor Series Sum: The calculated approximation of the function at the given x value using the specified number of terms.
  • Actual Function Value: The actual value of the selected function at the specified x value for comparison.
  • Absolute Error: The absolute difference between the Taylor series approximation and the actual function value.
  • Relative Error (%): The relative difference expressed as a percentage to illustrate the accuracy of the approximation concerning the actual value.

Use these results to analyze the effectiveness and accuracy of the Taylor series for the function and specified conditions.