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

please Help (Thinking)

Printable View

- Nov 10th 2010, 12:22 PMDreamer78692pointwise 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

please Help (Thinking) - Nov 10th 2010, 12:46 PMDrexel28
- Nov 10th 2010, 01:06 PMDreamer78692
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

Could you please help with this one - Nov 10th 2010, 01:13 PMDrexel28