(a) Show that ex 1 x for x 0 (b) Deduce that ex 1 x frac12 x2 for x 0 (c) Use mathematical induction to prove that for x 0 and any positive integer n, e 1 x 2 n

Question: (a) Show that ex > 1 + x for x > 0. (b) Deduce that ex > 1 + x ½ x2 for x >

(a) Show that ex > 1 + x for x > 0.
(b) Deduce that ex > 1 + x ½ x2 for x > 0.
(c) Use mathematical induction to prove that for x > 0 and any positive integer n,

e*>1+x++ 2! n!

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