Yes, that is correct. You can also write it as f(x) = 0 for x > 0 and f(0) = 1.

[Roni1985]

Homework Statement

f_n(x)= e^-n*x
Determine whether or not the sequence f_n converges pointwise for each x$$\geq$$0

Homework Equations

when a sequence of functions converges pointwise, the following is satisfied.
f(x)=lim_N->inff_n(x)

The Attempt at a Solution

I tried to graph it and I can see that the function shifts down closer and closer to y=0.

But, I can't really think of a mathematical proof here.

Thanks.

 

[snipez90]

Dang I thought this was going to be an actual PDE question. There is really no need to graph nor is there reason for mathematical proof unless you are clueless about the exponential function. Remember for pointwise convergence we only consider what happens by fixing an x in the set under consideration and then letting n approach infinity. Now fix x = 0, what is the limiting function here? Now fix an arbitrary x > 0, what happens when you let n go to infinity then?

 

[Roni1985]

Dang I thought this was going to be an actual PDE question. There is really no need to graph nor is there reason for mathematical proof unless you are clueless about the exponential function. Remember for pointwise convergence we only consider what happens by fixing an x in the set under consideration and then letting n approach infinity. Now fix x = 0, what is the limiting function here? Now fix an arbitrary x > 0, what happens when you let n go to infinity then?

Hello,

I'm sorry, my title is misleading. we just went over uniform and pointwise convergence before using it with PDEs :\

Thank you for the response.

That was also my logic.

So, I just say that f(x)= 1 for x=0 and 0 for x>0

?

Thanks.