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Ex 6.2

Ex 6.2, 1

Ex 6.2,2

Ex 6.2,3 Important

Ex 6.2,4

Ex 6.2, 5 Important

Ex 6.2, 6 (a)

Ex 6.2, 6 (b) Important

Ex 6.2, 6 (c) Important

Ex 6.2, 6 (d)

Ex 6.2, 6 (e) Important

Ex 6.2, 7

Ex 6.2,8 Important

Ex 6.2,9 Important

Ex 6.2,10

Ex 6.2,11

Ex 6.2, 12 (A)

Ex 6.2, 12 (B) Important

Ex 6.2, 12 (C) Important

Ex 6.2, 12 (D)

Ex 6.2, 13 (MCQ) Important

Ex 6.2,14 Important

Ex 6.2,15 You are here

Ex 6.2, 16

Ex 6.2,17 Important

Ex 6.2,18

Ex 6.2,19 (MCQ) Important

Last updated at April 14, 2021 by Teachoo

Ex 6.2, 15 Let I be any interval disjoint from [â1, 1]. Prove that the function f given by đ(đĽ) = đĽ + 1/đĽ is strictly increasing on I.I is any interval disjoint from [â1, 1] Let I = (ââ, âđ)âŞ(đ, â) Given f(đĽ) = đĽ + 1/đĽ We need to show f(đĽ) is strictly increasing on I i.e. we need to show fâ(đ) > 0 for đĽ â (ââ, âđ)âŞ(đ, â) Finding fâ(đ) f(đĽ) = đĽ + 1/đĽ fâ(đĽ) = 1 â 1/đĽ2 fâ(đĽ) = (đĽ2 â 1)/đĽ2 Putting fâ(đ) = 0 (đĽ2 â 1)/đĽ2 = 0 đĽ2â1 = 0 (đĽâ1)(đĽ+1)=0 So, đ=đ & đ=âđ Plotting points on number line The point đĽ = â1 , 1 into three disjoint intervals â´ f(x) is strictly increasing on (ââ , âđ) & (đ , â) Hence proved