2. Suppose that f is a measurable function satisfying 1 m({1 € R: \ƒ(1)| ≥ n}) ≤ /> > Is f integrable? nEN.

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Q: . If f : (0, 3) → R is continuous, must its range be an open (possibly infinite) interval?

A: See the detailed solution below.

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A:

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A: We have to determine whether the given function is continous for all values of x in R or not.

Q: VI. Let f(x)=x²-x²-x+1 on [-1,2]. Find all numbers c satisfying the conclusion to the Mean value…

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Q: 8. Let f(x) = x² if x ≤ 0 and f(x) = x + 1 if a > 0. At what points f: RR continuous? Here R is the…

A:

Q: 1. If f:(0, 3) → R is continuous, must its range be an open (possibly infinite) interval?

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Q: For what values of a, m and b does the function x = 0 0 <x<1 3, f(x) = }-x? + 3x + a, (mx+b, 1<xS2…

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Q: 2.23 Let 1 - x2 f(x): if x € Q, if r ¢ Q. Find all points p at which f is continuous. Prove your…

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Q: Let g and h be both differentiable functions. Also g, h e R. Suppose that g' = h and h' = -g on R.…

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A: Given,\

Q: Apply Definition 1.4 of Chapter IV to show that the function f(x) = 3x + 2 is integrable on the…

A: