1. ## pointwise limit.

if Fn(x) = x^(1/n) with Fn: [0,infinity) -> R

Find the pointwise limit of Fn(x)

this is what i have done:

x=0 Fn(x) -> 0
x!=0 Fn(x) -> 1

Is this correct... Im new to this so im not quite show about my answer

2. Originally Posted by Dreamer78692
if Fn(x) = x^(1/n) with Fn: [0,infinity) -> R

Find the pointwise limit of Fn(x)

this is what i have done:

x=0 Fn(x) -> 0
x!=0 Fn(x) -> 1

Is this correct... Im new to this so im not quite show about my answer

Ok, so how do you think we should show it (you're answer is correct)

3. Do you mean how I arrived at my answer???
If so I used a theorem that states that a(1/n) -> 1 as n -> infinity where a is an element of R.

Sorry there is a second part to this question that is:

Does Fn converge uniformly on [0,1]

My answer is no since sup|x(1/n)| -> 1 as n->infinity

AND

Does Fn converge uniformly on [1/2,1]

My answer is the same as above

I seriously doubt this is correct

4. Originally Posted by Dreamer78692
Do you mean how I arrived at my answer???
If so I used a theorem that states that a(1/n) -> 1 as n -> infinity where a is an element of R.

Sorry there is a second part to this question that is:

Does Fn converge uniformly on [0,1]

My answer is no since sup|x(1/n)| -> 1 as n->infinity

AND

Does Fn converge uniformly on [1/2,1]

My answer is the same as above

I seriously doubt this is correct

Well, it's surely not uniformly convergent since each of the $\displaystyle f_n(x)$'s is continuous but the limit isn't (this is on $\displaystyle [0,\infty)$) That said, I would try re-evaluating the second question.