Convergence of continuous function

[abisu]

Find:
limit as n goes to infinity of (limit as k goes to infinity of cos((n!*pi*x)^2k))

Since it's continuous, I know I should be able to move the limit inward, but I really can't see where to do that with this problem. The professor hinted that this problem will be on the final, so any help would be greatly appreciated. Many thanks.

 

[tkhunny]

Are you SURE you've written it correctly? No negative eponent? No zero, rather than "infinity"?

 

[abisu]

Unless the professor made a mistake when writing it on the board, then I wrote it correctly. Both go to infinity and no negative exponent. I spent a few hours working with a tutor on this problem and got nowhere. I really don't know where to start.

 

[tkhunny]

We're looking for a radius of convergence?

That cosine will not settle down if x is unbounded. The x is all we have to get the n and k under control.

 

[galactus]

Think about -1...1