only question 1&3

2 is not important please solve 1 and 3 to rate

I. The f (x) = ex function can be expressed in a Taylor series by 2! 3! n! Write a user-defined function y - Tavloz Exp(x) that determines the function by using the Taylor series representation. The input of the function is the value of the x and the output is the approximation of e at the given x. The user defined-function calculates the Taylor series hy adding terms of the series. If an is the nth term in the series, then the sum Sn of the n terms is SnSn-1 tan In each pass, the code calculates the estimated error E given by E script file callet TalexE to call TavlerExp and runs it. Run your code to evaluate e-2, e2, e3, e Sn- Sn-1 Sn-i and stop ading and stop adding terms when E 0.000001. Then write a 2. The factorial of a positive integer number is defined by n! n (n-1) (n-2)... (3) (2) (1), where 0!1. Write a user-defined function that calculates the factorial n! For function name and arguments, use yfact (x), where the input argument x is the given number and v is the value ofxl Write a script Caller fact.m which asks the user for the number. If the number is negative or non-integer, the error message should be displayed. Otherwise the fact will be called and the factorial of the given number will be calculated and displayed. Do not use MATLAB built-in function factorial0. Use fact with the following numbers a) 9! c) 0! d) -5! Hint: A number is non-integer when: floor(x)--x 3. The geometric mean GM of a set of n positive numbers x1, x2, ..., xn is defined by: GM= (x1 x2 m )1 Write a user-defined function that calculates the geometric mean of a set of numbers. The geometric mean is useful for calculating the average of rates. Thefollowing table gives the inflation rates in the US from 1978 to 1987 (inflation of 7.6% means 1.076). Use your user-defined function to calculate the average inflation for the ten year period ear 1978 19791980 1981 1982 1983 1984 1985 19861987 Inflation1.07611131135 1.103 1.062 1.03 1.043 1.036 1.019 1.036 rate