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Homework Statement Let f : (a, b) → R be a differentiable function and x0 ∈ (a, b). For any h > 0 small, there exists θ ∈ (0, 1), depending on h, such that f(x0 + h) = f(x0) + hf'(x0 + θh). If f is twice differentiable at x0 with f''(x0) != 0, prove that (a) lim h→0 (f(x0 + h) − f(x0) −...