If is differentiable with and and is continuous with as then prove that f is differentiable at 0.
So, from the definition we want to show that exists.
From we have
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If you are asking if that is a valid proof, yes, it is. Very well done! The one comment I would make is that the middle term in
is not necessay. Just set f(0) in equal to 0 to go directly:
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