Python. Solve for 1a and 1b

Let's start with a problem about dealing with floating point issues. 1a) Consider evaluating the function f(x) = log(1 + x)/x near x = 0. In particular, compute the value at x = le-16. In [1]: import numpy as np x = le-16; y = np.log(1 + x)/x Out[1]: 0.0 The computed result is zero. What is the error associated with this value? The correct value is very close to 1.0 and the relative error in the value above is close to 100%. Find an alternative (approximate) expression that is accurate for [x] in (). 1 x=1e40 2 y=1e40 ----> 3 print("(***10 + y**10) ** (1/10) gives ", (***10+y**10) ** (1/10)) OverflowError: (34, 'Result too large'). Provide an alternative version of the formula that avoids the overflow and provides an accurate value. In [ ]