L Hopital Iteration Count

Problem

To evaluate the limit of num(x) / den(x) at x0, apply L'Hopital's rule repeatedly until the denominator is nonzero at x0, then evaluate the ratio of derivatives.

Given coefficient lists in ascending order and x0, return [applications, limit], where applications is the number of differentiations (capped at 10) and limit is None if the denominator remains zero after the cap.

Hint

Differentiate numerator and denominator together and count the rounds.

Test cases

case 1

in: [[-1,0,1],[-1,1],1]

expected: [1,2]

case 2

in: [[-2,0,0,1],[-1,0,1],1]

expected: [1,1.5]

case 3

in: [[1,0,0],[1,0],0]

expected: [0,1]

Starter codePython

def lhopital_iteration_count(num, den, x0):
    # Your code here
    pass

3 test cases · run your code against them in the editor