Ex 6.2

Ex 6.2, 1

Ex 6.2,2

Ex 6.2,3 Important You are here

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

Ex 6.2,18

Ex 6.2,19 (MCQ) Important

Last updated at April 16, 2024 by Teachoo

Ex 6.2, 3 Find the intervals in which the function f given by f (𝑥) = sin 𝑥 is (a) strictly increasing in (0 , 𝜋/2) f(𝑥) = sin 𝑥 f’(𝒙) = cos 𝒙 Since cos 𝑥 > 0 for 𝑥 ∈ ("0 , " 𝜋/2) ∴ f’(𝑥) < 0 for 𝑥 ∈ (0 , π) Thus, f is strictly increasing in ("0 , " 𝜋/2) Rough cos 0 = 1 cos 𝜋/4 = 1/√2 cos 𝜋/2 = 0 Value of cos𝑥 > 0 for (0 , 𝜋/2) Ex 6.2, 3 Find the intervals in which the function f given by f (𝑥) = Sin x is (b) strictly decreasing (𝜋/2,𝜋)f(𝑥) = sin 𝑥 f’(𝒙) = cos 𝒙 Since cos 𝑥 < 0 for 𝑥 ∈ (𝜋/2 , 𝜋) ∴ f’(𝑥) < 0 for 𝑥 ∈ (𝜋/2 " , π" ) Thus, f is strictly decreasing in (𝜋/2 " π" ) Rough cos 𝜋/2 = 0 cos 3𝜋/4 = co𝑠 ("π − " 𝜋/4) = – cos𝜋/4 = (−1 )/√2 Value of cos 𝑥 < o for 𝑥 ∈ (𝜋/2 , 𝜋) Ex 6.2, 3 Find the intervals in which the function f given by f (𝑥) = sin x is (c) neither increasing nor decreasing in (0, π)(0 , π) = (0 , 𝜋/2) ∪ (𝜋/2,𝜋) From 1st part f(𝑥) is strictly increasing in (0 , 𝜋/2) And from 2nd part f(𝑥) is strictly decreasing in (𝜋/2,𝜋) Thus, f(𝒙) is neither increasing nor decreasing in (0, π)