stupid_girl
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A new one
Hey you can't just commute the limit with the integral like that. Everyone knows limits don't commute in general.Taking limit
It requires uniform convergence. Does the syllabus cover techniques to prove uniform convergence?Hey you can't just commute the limit with the integral like that. Everyone knows limits don't commute in general.
Please justify the commutation using only techniques from the syllabus.
It is too abstract. I'll leave it for your university lecturer and tutor.@stupid_girl teach us
Is that another way of saying “the proof is left as an exercise for the reader”?It is too abstract. I'll leave it for your university lecturer and tutor.
This one isn't too hard, right? The same old trick applies.A new one
It seems no one has attempted yet. It's actually a combination of several results. The last one is the most interesting.This question can take ages if you're not on the right track.
(modified to make it look more evil...feel free to share your attempt)
I got this one, it's quite a standard one especially compared to all the other ones.Last question of the year
Show by mathematical induction that
for all positive integers n and non-zero real number a.
Let's use the same old trick that has appeared in this thread many times.My first question
How about something a little bit different?
Without numerically evaluating , show that
The well known inequality may be useful.