Recall that if f (t) g(t) for t 0, then for all x 0, x 0 f (t) dt x 0 g(t) dt 7 The
Chapter 5, Problem 75(choose chapter or problem)
Recall that if f (t) g(t) for t 0, then for all x 0, x 0 f (t) dt x 0 g(t) dt 7 The inequality et 1 holds for t 0 because e > 1. Use (7) to prove that ex 1 + x for x 0. Then prove, by successive integration, the following inequalities (for x 0): ex 1 + x + 1 2 x2, ex 1 + x + 1 2 x2 + 1 6 x3
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