Let N be a nonempty set and B a o-ring on N. Let µ, v be two measures on B and μ(A) < ν(Α), A € B. Show that fdµ < / fdv or all nonnegative measurable f :N→ [0, ∞0].

Q: Let T~ tn, where n is the degrees of freedom. Assume c satistifies P(|T| > c) =0.05. If n = 4, then…

A: The question is about t distribution.Given :degree of freedom ( n ) = 4To find :1 ) Value of ( a ) =…

Q: Let (X, M, µ) be a measure space such that uX = 1, and let f : X → (0, 1). Show that u) / fdµ 2 1

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Q: Let h: R→ R be continuous on R satisfying h(m/2") = 0 for all me Z, ne N. Show that h(x) = 0 for all…

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Q: Is the following bounded or unbounded and why? f(x,y) = ln(x2 + y2)

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Q: 2. Show that the function, defined by f(x) = is NOT uniformly continuous on its x2 %3D domain D(f) =…

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Q: Suppose f and g are continuous on [a, b] and f f(x) dx = S% 8(x) dr. Prove that there is cE [a, b]…

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Q: 6. Let f(x) = n for all x € ((n + 1)-¹, n−¹], n = 1, 2,.... Prove that f is not integrable on (0,…

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Q: Evaluate function given assuming ƒ is integrable on [a, b].

A: We have to calculate,∫abf(x)dx+∫baf(x)dx = ?            ...................(1)As function f(x) is…

Q: Q \ Let f: [0,2] → R be defined by 1, x € [0,1), 1 f(x) = x = 1, 2' 0, хе (1,2], and let the…

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Q: 1. Let f(x) = x. Show that f is uniformly continuous on any finite closed interval [a, B] (Hint: x-y…

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Q: Evaluate the definite integral using the Fundamental Theorem of Calculus. 64 (1 Vx)2 dx 16 2x

A: we need to evaluate ∫16641 - x22x   using fundamental theorem of calculus if F(x) be any…