: Iff [a, b] →→ R is integrable, then there exists a sequence Pn of partitions of [a, b] for which lim U(f, Pn) - L(f, Pn) = 0 n→∞0

Q: Let X be a normed space and let 0x0 EX. Show that there is f = X* such that f(x) = 1 and ||f|| =…

A: Given, a normed space  and .It is required to show that, there exists  (the dual space of ) such…

Q: Given a continuous function f:[0,1]→R, define its sequence of Bernstein polynomials. Please be as…

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Q: (b) Give an example of a bounded function f on [a,b] for which f2 e R[a,b), but f is not in R[a,b).

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Q: A bounded function f: A R is integrable if and only if for every e > 0 there is a partition P of A…

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Q: f Let f:(R,1,) - (R,T,), f(x) = x². Find f-(a, b) and then show that is continuous on R.

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Q: Recall that the Möbius product of two functions f, g: N→ R is the function f*g: N→ R given by…

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Q: Find an example of a function f : [−1,1] → R such that for A := [0,1], the restriction f |A(x) → 0…

A: To give an example of a function f : [−1,1] → R such that for A := [0,1], the restriction f |A(x) →…

Q: a. Is it possible for a continuous function f on [0,1] to have Lf(P) = 4 and Uf(P) = 3 for some…

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Q: Suppose that f1 : [0, 1] → R and f2 : [0, 1] → R are continuous everywhere and that f1(0) f2(1).…

A: Intermediate value theorem : Suppose be a continuous function then it takes all values between .

Q: Let X = N, A= (2,3..4) and d(r, y) = |2- y| Find limit pointa of A. d(A) = (2) o NO

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