For this assignment you are to write a MATLAB script to find the Taylor Series expansion...

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For this assignment you are to write a MATLAB script to find the Taylor Series expansion of e*. Taylor Series are infinite sums that converge to a particular value. In this problem you will use: e=1+x+2+ Where the terms in the denominators (i.e., 2!) are factorials and are found as follows: for example Modify the provided MATLAB template as follows: + + x! = x*(x-1)*(x-2)....(1) 3! = 3*2*1 A. Add a function to the script called "TaylorSeriesElement" This function should receive the value of x and its power and return a component of the Taylor series such as x^2/2!. To find the factorial use the MATLAB function - factorial(i). This returns the factorial of the value i. In this case it will be the power sent to the function. B. Add a for-loop that repeats a set number of times and calls the function "TaylorSeriesElement" on each iteration. That result is stored in an array. Call that array "taylorSeries." C. Add a second function called "SumSeries. That function should return the sum of the Taylor Series. Note that the array will actually start at they second term in the series, so don't forget to initialize the sum to 1. D. Set x = 2 and use this script to find the amount of terms required to get within 4 decimal points of the MATLAB function for the exponential. In this case it is exp(x). The table below shows the first few summations and can be used to validate your script. Terms 1+2 Result 3 22 5 1+2+ 21 23 23 1+2+ +=+ 6.3333..... 21 3! Table 1 Examples - For this assignment you are to write a MATLAB script to find the Taylor Series expansion of e*. Taylor Series are infinite sums that converge to a particular value. In this problem you will use: e=1+x+2+ Where the terms in the denominators (i.e., 2!) are factorials and are found as follows: for example Modify the provided MATLAB template as follows: + + x! = x*(x-1)*(x-2)....(1) 3! = 3*2*1 A. Add a function to the script called "TaylorSeriesElement" This function should receive the value of x and its power and return a component of the Taylor series such as x^2/2!. To find the factorial use the MATLAB function - factorial(i). This returns the factorial of the value i. In this case it will be the power sent to the function. B. Add a for-loop that repeats a set number of times and calls the function "TaylorSeriesElement" on each iteration. That result is stored in an array. Call that array "taylorSeries." C. Add a second function called "SumSeries. That function should return the sum of the Taylor Series. Note that the array will actually start at they second term in the series, so don't forget to initialize the sum to 1. D. Set x = 2 and use this script to find the amount of terms required to get within 4 decimal points of the MATLAB function for the exponential. In this case it is exp(x). The table below shows the first few summations and can be used to validate your script. Terms 1+2 Result 3 22 5 1+2+ 21 23 23 1+2+ +=+ 6.3333..... 21 3! Table 1 Examples -