Hospital Rule (某法则求 0:0 或 ∞:∞ 极限)

When you encounter some limitation formulas after giving approaching x seems like or , you can get its molecular and denominator's first derivative partly, then do this process again and again until you get some limitation value that not seems like or

formula = a fractional limitation formula
molecular, denominator = split_fraction(formula)

while True:
    i = 0

    molecular_limitation_value = get_limitation_value(molecular)
    denominator_limitation_value = get_limitation_value(denominator)

    if '{m}:{d}'.format(m=molecular_limitation, d=denominator) in ['0:0', '∞:∞']:
        molecular = take_first_derivative(molecular)
        denominator = take_first_derivative(denominator)
        i += 1
    else:
        return molecular_limitation_value / denominator_limitation_value

    if i > 999:
        print("You can't use hospital rule in this formula.")


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