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## Homework Statement

What would be the limit of {cos(m!*pi*x}^{2n} as 'n' and 'm' go to infinity along with proof? Also x is real. I have no clue as to how to start the question. Please help! Thanks.

## The Attempt at a Solution

I tried to write the original function as e^[(ln(cos(m!*pi*x)/(1/2n)], but since not both the numerator and denominator go to zero, I couldn't use L'Hopital's Rule.

Other method I tried was using the power series expansion of cosine, but I am not sure how to deal with m!

Any hints or help will be greatly appreciated. Thanks!