Question: (a) Use the Taylor series for e x at x = 0 to show that e x > x 2 /2 for x > 0.

(a) Use the Taylor series for ex at x = 0 to show that ex > x2/2 for x > 0.

(b) Deduce that e-x < 2/x2 for x > 0.

(c) Show that xe-x approaches 0 as x → ∞.

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