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Timeless Theorems of Mathematics/Differentiability Implies Continuity
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Statement: If a function is differentiable at the point then is continuous at
Proof: Assume is differentiable at . Then, exists.
The function is continuous at when
So, to prove the theorem, it is enough to prove that
Therefore, When exists, is true.
If is differentiable at the point then is continuous at [Proved]