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 -