Which of the following statements is absolutely false. A. For a continuous function f, ∫a0f (a − x) dx = ∫a0f (x) dx. B. The net change of a differentiable function f in the interval [0, a] is a0f ′ (x) dx. C. The average value of a differentiable function f in the interval [0, a] is 1 / a * ∫a0f ′ (x) dx. D. If a continuous function f satisfies f (x) + f (a − x) = b at each point x∈ [0, a], then ∫a0f (x) dx = a * b / 2. E. None F. The average change of a differentiable function f in the interval [0, a] is 1a∫a0f ′ (x) dx.

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A:

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.