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Divam Kumar posted an Question
December 01, 2020 • 21:04 pm 30 points
  • IIT JAM
  • Mathematics (MA)

23. a sequence of functions un 1s said to converge uniformly on an interval |a, b] to a function fif for any e> 0 and for all x ela, b} there exists an integer

23. A sequence of functions Un 1s Said to converge uniformly on an interval |a, b] to a function fif for any e> 0 and for all x ela, b} there exists an integer N such that for all x e [a, b]: (A) f)-f)] E, n2N (C) 1f.)-f)) =6, n2N (D) None of these 24. The sequencee J wheree nx fnx) = nxe, n = 1,2,3, ... converges pointwise to: (A) 1 (B) 0 (C)-1 (D) None of these 25. In a metric space (X, d) for all x in X: (A) d(r, x) =1 (B) dt, x)=-1 (C) dx, x) >0 (D) d, x) = 0 26. If f (x, y) = 2xr -xy +2jy, then findf, at the point (1, 2). (A) 1 (B) 3 (C)2 (D) 2 27. Iffis a differentiable function, then (A) fis not continuous (B) fis continuous (C) limit at (0, 0) does not exist (D) None of these 28. If f(x, y) = 2x-xy+2y, then find f, at the point (1, 2). (A) 1 (B) 3 (C)-2 (D) 7

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