Question

1) Write and test a well-commented Python function, called “myexp” that approximates the value for the function ?(?) = ? ? . This function can be approximated by a Taylor series ? ? ≈ ∑ ? ? ?! ∞ ?=0 , and recall that the factorial function is given by the recursive relationship ?! = ? (? − 1)!, ?ℎ??? ? ∈ ??? ≥ 0, ??? 0! = 1

1. You will need to write your own factorial function, and you should call it “myfact”. Note this was a lecture demo.

2. Write your own function for approximating the exponential function and check your function’s results with the built-in Python function math.exp(x).

3. Your function should use enough terms in the Taylor series such that the last term added before returning a result should be smaller than 0.0001. In other words, your code should compute the Taylor series using a “while” loop that uses the size of the term being added to the series is the stopping criteria.

Answer 1

`Hey,

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import math
def myfact(n):
if(n==0):
return 1;
return n*myfact(n-1);
def myexp(x):
s=0;
t=20;
i=0;
while(abs(t)>0.0001):
t=(x**i)/myfact(i);
i=i+1;
s=s+t;
return s;
x=0.8;
print("Error is",abs(myexp(x)-math.exp(x)))

Kindly revert for any queries

Thanks.