Help with a, b, and c please 1.a) For 0 ≤ x ≤ 1, show thatx²<

Answered: Image /qna-images/answer/63cbc30e-208c-4e75-9470-8eb08bd9be2d.jpg

a) For 0 ≤ x ≤ 1, show that < x². √2 + x b) Use the estimate in a) and integrate it to prove that 3/2²/²drs ² < =dx 3√2 √1+x 3 c) By estimating 2x/ sinä on the interval [π/6, π/2], prove that 27² T/2 2x 4π² [1² 9 9 x² sin x

a) For 0 ≤ x ≤ 1, show that < x². √2 + x b) Use the estimate in a) and integrate it to prove that 3/2²/²drs ² < =dx 3√2 √1+x 3 c) By estimating 2x/ sinä on the interval [π/6, π/2], prove that 27² T/2 2x 4π² [1² 9 9 x² sin x

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter2: The Integers

Section2.4: Prime Factors And Greatest Common Divisor

Problem 25E: Prove that if m0 and (a,b) exists, then (ma,mb)=m(a,b).

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Question

Help with a, b, and c please

1.
a) For 0 ≤ x ≤ 1, show that
x²
<
<x².
√2
+ x
b) Use the estimate in a) and integrate it to prove that
1
x²
S
-dx ≤
3√2
+x
3
c) By estimating 2x/sinx on the interval [π/6, π/2], prove that
pπ/2 2x
4π²
27²
9
9
<
x²
sin x

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