Taylor's theorem with remainder

 Objectives:

1. Use Taylor polynomial to approximate a function and its value

b. Estimate the remainder of a Taylor series approximation of a given function

The interesting thing about representing a function by different Taylor polynomials is that these Taylor polynomials represent an approximation of the given function. The Taylor polynomial representation of a function allows also approximate the values of a function. The Taylor theorem with remainder allows to estimate the remainder of the Taylor series approximation of a given function. 

Taylor theorem with remainder

Example

Solution

The function and the Taylor polynomials are shown here:

Practice