III. Let f be continuous on [a, b] and differentiable almost everywhere on (a, b). Suppose there is a nonnegative function g that is integrable over [a, b] and Diff1/nf ≤g a.e on [a, b] for all n. [ƒ = f(b) – ƒ(a). Show that

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III. Let f be continuous on [a, b] and differentiable almost everywhere on (a, b). Suppose
there is a nonnegative function g that is integrable over [a, b] and
Diff1/nf ≤g a.e on [a, b] for all n.
Show that
[*f' = f(b) – f(a).
a
Transcribed Image Text:III. Let f be continuous on [a, b] and differentiable almost everywhere on (a, b). Suppose there is a nonnegative function g that is integrable over [a, b] and Diff1/nf ≤g a.e on [a, b] for all n. Show that [*f' = f(b) – f(a). a
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