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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

Ex 6.2, 16

Ex 6.2,17 Important You are here

Ex 6.2,18

Ex 6.2,19 (MCQ) Important

Last updated at March 16, 2023 by Teachoo

Ex 6.2, 17 Prove that the function f given by f (đĽ) = log cos đĽ is strictly decreasing on (0,đ/2) and strictly increasing on(đ/2,đ) f(đĽ) = log cos đĽ We need to show that f(đĽ) is strictly decreasing on (0 , đ/2) & strictly increasing on (đ/2 , đ) i.e. We need to show fâ(đ) < 0 for đĽ â (đ , đ /đ) & fâ(đ) > 0 for đĽ â (đ /đ , đ ) Finding fâ(đ) fâ(đĽ) = (đđđ.cosâĄđĽ )â fâ(đĽ) = (1 )/cosâĄđĽ . đ(cosâĄđĽ )/đđĽ fâ (đĽ) = 1/cosâĄđĽ .ăâsinăâĄđĽ fâ (đ) = ăâđŹđ˘đ§ăâĄđ/đđđâĄđ Checking sign of fâ (đĽ) on (0 , đ/2) & (đ/2 , đ) For 0 < đ < đ /đ Here, x is in the 1st quadrant â´ cos đĽ > 0 & sin đĽ > 0 Now, fâ(đĽ) =ăâđŹđ˘đ§ăâĄđ/đđđâĄđ = ((â)(+))/((+) ) < 0 Hence, fâ(đ) < 0 for đĽ â (0 , đ/2) Thus f(đĽ) is strictly decreasing for đĽ â (0 , đ/2) For đ /đ < đ < Ď Here, x is in the 2nd quadrant â´ cos đ < 0 & sin đ > 0 Now, fâ(đĽ) =ăâđŹđ˘đ§ăâĄđ/đđđâĄđ = ((â)(+))/((â) ) > 0 Hence, fâ(đ) >0 for đĽ â (đ/2 , đ) Thus, f(đĽ) is strictly increasing for đĽ â (đ/2 , đ)