# Differentiability and Limits

Please see the attached file for the fully formatted problems.

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

https://brainmass.com/math/calculus-and-analysis/differentiability-limits-16488

#### Solution Preview

Please see the attached file for the complete solution.

Thanks for using BrainMass.

, ...

#### Solution Summary

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

$2.19