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Divam Kumar posted an Question
December 01, 2020 • 21:02 pm 30 points
  • IIT JAM
  • Mathematics (MA)

59. let fbe an integrable function over [a, b] and m be the upper bound of f in [a, b], then (a) f de 2 m(b- a) (b) de = m(b- a) (c)fd s m(b - a) (d) none of th

59. Let fbe an integrable function over [a, b] and M be the upper bound of f in [a, b], then (A) f de 2 M(b- a) (B) de = M(b- a) (C)fd s M(b - a) (D) None of these 60. Let P be a partition of [a, b], M be the upper bound of f in [a, b], U (P) be the upper sum offto the partition P. Then: (A) M (b-a) 2 U (p.f (B) M (b-a)=U (p,J (C) M(b-a) s U (p,) (D) None of these 61. If f and fy are both differentiable at a point (a, b), then by Young's theorem: (A) Sya, b) = Sa(a, b) (B) a, b) = -Jyp(a,b) (C) Sa,b) * Sn(a, b) (D) None of these 62. If a series Jn converges uniformly to f on la, b] and each term n() is integrable on [a, b], then: (A) S sd-- S,a. VxE [a, b] (B)Jsd-U,d Vxe [a,b] Vxe [a, b] (D) None of these 63. A bounded function, having a finite number of points of discontinuity on [a, b], is on [a, b]. (A) integrable (B) not integrable (D) None of these (C) differentiable (15) XE(H-3)-MAT(5)

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