Is the Function Uniformly Convergent on (0,1]?

[hmmmmm]

I am given $$f_n(x)=\frac{nx}{nx+1}$$ defined on $$[0,\infty)$$ and I have that the function converges pointwise to $$0 \ \mbox{if x=0 and} 1\ \mbox{otherwise}$$

Is the function uniform convergent on $$[0,1]$$?

No. If we take x=1/n then $$Limit_{n\rightarrow\infty}|\frac{1/n*n}{1+1/n*n}-1|=0.5$$

which implies that $$Limit_{n\rightarrow\infty} sup |f_n(x)-1|$$ is not 0.

I am then asked if it converges uniformly on the interval $$(0,1]$$ which I think it does but how do I show that $$Limit_{n\rightarrow\infty} sup |f_n(x)-1|$$=0?

thanks for any help

 

[mathman]

Your latex is screwed up.

 

[hmmmmm]

Yeah do you know why that is?

thanks for any help

 

[willem2]

Yeah do you know why that is?

thanks for any help

don't put TEX in capitals.