1. Prove that if u and v are differentiable functions of x, and u 0, then 2. [HARDER] If f(x) = ex _ 1 _ x, then f (x) = ex _ 1 0 for all x 0. The function f(x) is therefore strictly increasing in the interval . Since f(0) = 0, it follows that f(x) 0 for all x 0, and so ex 1 + x for all x 0. Use the same method to prove the following inequalities:
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