So here we have a contest for all the calculus lovers. I have already posted 2 challenges of this contest. I will be posting at least one challenge each week. When this contest will end is not yet decided but that's unimportant.

I will make a set and put challenges in it. The challenges will all be generalizations. All you have to do is to post proofs of the claims I give. The more proofs a person gives in the whole set, higher he/she goes in the Leaderboard.

Here's the set -

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