Use MATLAB fuctions to solve this The Taylor series of exp (x) can be expanded a
ID: 3797217 • Letter: U
Question
Use MATLAB fuctions to solve this
The Taylor series of exp (x) can be expanded as following e^x = Sigma^infinity_n = 1 x^n/n! = 1 + x/1! + x^2/2! + x^3/3!+... Task 1: Write a custom function to calculate exp(x) with the two input arguments are x and n (where n is the number of terms) and one output argument is the value of exp(x). Task 2: Use the function in task 1 to calculate exp(2) with 3 terms and exp(3) with 6 terms. Task 3: Calculate the error percentage between the result of exp(3) with 3 terms from task 2 and the result of exp(3) using the built-in exp() function in Matlab. If you want the error less than 0.001%, how many terms will be needed?Explanation / Answer
Task 1 :
..................
function e = exponential(x, n)
e = 0;
for i = 0:n
e = (e + x.^i/factorial(i));
end
end
Task 2 (Add these below call statements in function)
........
exponential(2, 3)
exponential(3,5)
ans = 6.3333
ans = 19.412
Task 3 (Now modify the program by using below statements)
.........
l = exponential(2,3)
q = exponential(3,6)
v = exp(2)
u = exp(3)
errorPer1 = ((v - l)/100)
errorPer2 = ((u - q)/100)
l = 6.3333
q = 19.412
v = 7.3891
u = 20.086
errorPer1 = 0.010557
errorPer2 = 0.0067304
..........................................................
Now to check the error less than o.oo1% in both case
...............................................
l = exponential(2,4)
q = exponential(3,7)
v = exp(2)
u = exp(3)
errorPer1 = ((v - l)/100)
errorPer2 = ((u - q)/100)
l = 7
q = 19.846
v = 7.3891
u = 20.086
errorPer1 = 0.0038906
errorPer2 = 0.0023911
...............................
l = exponential(2,5)
q = exponential(3,8)
v = exp(2)
u = exp(3)
errorPer1 = ((v - l)/100)
errorPer2 = ((u - q)/100)
l = 7.2667
q = 20.009
v = 7.3891
u = 20.086
errorPer1 = 0.0012239
errorPer2 = 7.6385e-04
.................................
l = exponential(2,6)
q = exponential(3,8)
v = exp(2)
u = exp(3)
errorPer1 = ((v - l)/100)
errorPer2 = ((u - q)/100)
l = 7.3556
q = 20.009
v = 7.3891
u = 20.086
errorPer1 = 3.3501e-04
errorPer2 = 7.6385e-04
So , to get the error less than o.001 %, For exp(2) we need 6 terms and for exp(3) we need 8 terms.
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