f fn → ƒ uniformly and the functions fn have only jump discon- sinuities, prove that f has only jump discontinuities.

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Q: Show

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Q: 24. Show that f(x) = mx + b, where m,b e R, is uniformly continuous on R. %3D

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Q: 5. Let fn(x) ". Show that z"0 uniformly on (0, ).

A: We have to use squeeze theorem here.

Q: 1. Show that if f [a, b] → R is increasing, then f is of bounded : variation.

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Q: Let fn (æ) = a" – x2", defined on [0, 1] %3D is pointwise converges to f (x) = 0, on [0, 1] then ||…

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Q: If f is integrable, then f is continuous. Select one: a. True b. False

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Q: 3. Suppose f, g:D → R continuous on D. are uniformly continuous on D. Prove that f + g is uniformly

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Q: 1. Show that if f [a,b] → R is increasing, then f is of bounded variation.

A: Given f: a, b → ℝ is increasing function.

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Q: 4. Suppose fn:A→ Ris uniformly continuous on A , Vn e N and fn →f converges uniformly on A.…

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Q: 2 Q/if the function fc)=ĕ is not Continuous at T where =TIL x<T foint the fourier Scries of fcxeě is…

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Q: ve that the Bessel functionm generating funchion ie too

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Q: Find aland U so that the function S 7z³ – 3x² + 7, z -2 is both continuous and differentiable. al =

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Q: 1. Show (in terms of -5) that a function f: [2, 7] R be defined by f(r) V+1 is uniformly continuous.

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Q: Suppose f and g are continuous functions. Provide an example such that | g(x)dr diverges 0. adf(x)dr…

A: Follow next step

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Q: Let                          fn(x) = nx/1 + nx2  (d) Is the convergence uniform on (1,∞)?

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Q: b) Use the Comparison Theorem with f(x) = - to show whether , g(x)dx is convergent or divergent.

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Q: Let f(x) = x² In x, where x > 0. Show that f(x) has only one critical point.

A: Given data: The given function is f(x)=x2lnx. The critical point is the point where the slope of the…

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