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Calculus/Help getting h out of the denominator

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Expert: - 10/14/2009


Question
limit[h:0,((x+h)^4-(x^4))/(h)]

Answer
NOte that (x+h)^4 = x^4 + 4x^3h + 6x^2h^2 + 4xh^3 + h^4.

When x^4 is subtracted off, the result is 4x^3h + 6x^2h^2 + 4xh^3 + h^4.

When divided by h, the result is  4x^3 + 6x^2h + 4xh^2 + h^4.

As h goes to 0, the answer is only 4x^3, for the rest of the terms have a zero in them.

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