Ashwini posted an Question
July 28, 2020 • 21:53 pm 30 points
  • IIT JAM
  • Mathematics (MA)

1. use seq uential criterion for limits to show that the following limits do not exist. (i) lim cos (ii) lim sin , (iii) liml+sin (iv) lim asgn cos a 0 0 hint.

1. Use seq uential criterion for limits to show that the following limits do not exist. (i) lim cos (ii) lim sin , (iii) liml+sin (iv) lim asgn cos a 0 0 Hint. (ii) Take an = +2nT; yn = +2nT. (iv) Talke tn = 2nT; yn = T+ 2nT.

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    Deepak singh 1 best-answer

    see attached part 1 , 2,3 and 4

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    since sequence an = (1/n ) is convergent sequence but f(an) is not convergent , so limit doesn't exist

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    put the sequence 1/ n in function , we find that f(1/n) is not convergent , that's why f(x) =(1/x)sin(1/x) has no limit..

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