Use Exercise 86 to show that e^x/x² ≥ x/6 and conclude that  Then use Exercise 87 to prove more generally that

Data From Exercise 86 

Recall the following property of integrals: If ƒ(t) ≥ g(t) for all t ≥ 0, then for all x ≥ 0,

Data From Exercise 87

Generalize Exercise 86; that is, use induction (if you are familiar with this method of proof) to prove that for all n ≥ 0,

ex lim = 0. -2 x-00x