Thread: Pointwise limits

I'm trying to understand how to do pointwise limits
a)f_n(x)=nx/(1+nx^2)
b)g_n(x)=(nx+sin(nx))/2n
lim[1/2+sin(nx)/2n)]
c)h_n(x)=x/(1+x^n)
d)f_n(x)=1 if |x|>=1/n
=n|x| if |x|<1/n

When you study pointwise limits, is a constant.

For example



Also, you can conclude the convergence isn't uniform on 'cause each is continuous but the limit is not continuous.