Solution-A differentiable function on an interval of the

A differentiable function on an interval of the form

Reference no: EM13527450

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)) .

Reference no: EM13527450

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A differentiable function on an interval of the form

Reference no: EM13527450

Reference no: EM13527450

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