# Math Help - Pointwise limit

1. ## Pointwise limit

If possible, find the pointwise limit for the following sequences ({ $f_{n}$} $_{n \in N}$:

a) where for each n $\in$ N the function $f_{n}$: [-1,1] $\rightarrow$ R is given by $f_{n}(x) = \frac{nx}{1 + n^2(x^2)}$

b) where for each n $\in$ N the function $f_{n}$: R $\rightarrow$ R is given by
$f_{n}(x)$ =
1 if x $\in$ [-n,n]
or 0 if otherwise

2. a) $f_n$ 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 $f_n$ tend to 0.
b) $f_n$ 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, $f_n(x)=1$, so it tend to 1 for any x in R.