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Ex 6.2
Ex 6.2,2
Ex 6.2,3 Important
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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 You are here
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 Aug. 19, 2021 by Teachoo
Maths Crash Course - Live lectures + all videos + Real time Doubt solving!
Ex 6.2, 12 Which of the following functions are strictly decreasing on (0,𝜋/2) ? (B) cos 2𝑥 Let f(𝑥) = cos 2𝑥 Finding f’(𝒙) f’(𝑥) = (cos2𝑥 )′ f’(𝑥) = –2 sin 2𝑥 Let 2𝑥 = θ ∴ f’(𝑥) = –2 sin θ When 0 < x < 𝜋/2 , then 0 < θ < 𝜋 Since sin θ > 0 for 0 < θ < 𝜋 Therefore, sin 2x > 0 for 0 < 2x < 𝜋 Multiplying −2 both sides −2 × sin 2x < −2 × 0 for 0 < 2x < 𝜋 −2 sin 2x < 0 for 0 < 2x < 𝜋 f’(x) < 0 for 0 < 2x < 𝜋 f’(x) < 0 for 0 < x < 𝝅/𝟐 Therefore, f(x) is strictly decreasing for 𝒙 ∈ (𝟎 , 𝝅/𝟐)