If possible, find the pointwise limit for the following sequences ({ } : a) where for each n N the function : [-1,1] R is given by b) where for each n N the function : R R is given by = 1 if x [-n,n] or 0 if otherwise
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a) tend to 0 for any x in [-1,1]: for if x=0, obviously, it tend to 0; if x=\=0, then nx tend to infinity, and tend to 0. b) tend to 1 for any x in R: for any given x in R, there is N such that |x|<N, then if n>N, , so it tend to 1 for any x in R.
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