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Differentiability and Limits

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Let f: I →ℜ where I is an open interval containing the point c, and let k ∈ ℜ. Prove the following
1. f is differentiable at c with f ′(x) = k iff lim h→0 [f(c+h) - f(c)]/h=k
2. If f is differentiable at c with f ′(c) = k , then lim h→0 [f(c+h) - f(c-h)]/2h=k

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A proof involving differentiability and limits is provided. The solution is detailed and well presented.

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