Prove that for all x > 0 and all positive integers nx2e* > 1+x +2!+3x"3!n!Recall that n! = n(n – 1)(n – 2)..3 · 2 · 1.HINT: e = 1+/edt > 1+ f dt = 1+xHINT: e* =1+e* = 1+e' dt > 1+ | (1+t)dtx2= 1+x +2and so on.

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Prove that for all x > 0 and all positive integers n x2 e* > 1+x + 2! +3 +: 3! x" + n! Recall that n! = n(n – 1)(n – 2) · . -3 · 2 · 1. | х HINT: e* = 1+ e'dt > 1+ dt = 1+ x eʻ = 1+ [ e | (1+ t)dt e'dt > 1+ x2 = 1+x + - and so on.

Prove that for all x > 0 and all positive integers n x2 e* > 1+x + 2! +3 +: 3! x" + n! Recall that n! = n(n – 1)(n – 2) · . -3 · 2 · 1. | х HINT: e* = 1+ e'dt > 1+ dt = 1+ x eʻ = 1+ [ e | (1+ t)dt e'dt > 1+ x2 = 1+x + - and so on.

Algebra for College Students

10th Edition

ISBN:9781285195780

Author:Jerome E. Kaufmann, Karen L. Schwitters

Publisher:Jerome E. Kaufmann, Karen L. Schwitters

Chapter9: Polynomial And Rational Functions

Section9.2: Remainder And Factor Theorems

Problem 52PS

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Question

Prove that for all x > 0 and all positive integers n
x2
e* > 1+x +
2!
+3
x"
3!
n!
Recall that n! = n(n – 1)(n – 2)..3 · 2 · 1.
HINT: e = 1+/edt > 1+ f dt = 1+x
HINT: e* =1+
e* = 1+
e' dt > 1+ | (1+t)dt
x2
= 1+x +
2
and so on.

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