Let f be a differentiable function on an interval of the form (a, +∞). Prove that if there is a number r not equal to 0 such that limx→∞(rf′(x) + f(x)) = L is finite, then limx→∞ f′(x) = 0 and limx→∞ f(x) = L. Hint: apply L'Hˆopital's Rule to [e^(x/r) x f(x)]/(e^(x/r)) .