Question: 2. Suppose that a continuous function f : (a, b) - R is differentiable except possibly at ro E (a, b), and that lim,-+1. f'(x)

2. Suppose that a continuous function f : (a, b) - R is differentiable except possibly at ro E (a, b), and that lim,-+1. f'(x) = L exists. Prove that f'(ro) = L. [Warning: It is NOT TRUE in general that lim,-+ limy-+. f(x, y) = limy-+& lim,-+a f(x, y), even for beautiful functions f(x, y). Don't switch the order of nested limits without careful checking!]

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