Ex 6.4, 1 (iv) - Find approximate value of (0.009)^1/3 - Ex 6.4

Ex 6.4, 1 (iv) - Chapter 6 Class 12 Application of Derivatives - Part 2
Ex 6.4, 1 (iv) - Chapter 6 Class 12 Application of Derivatives - Part 3
Ex 6.4, 1 (iv) - Chapter 6 Class 12 Application of Derivatives - Part 4

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Question 1 Using differentials, find the approximate value of each of the following up to 3 places of decimal. (iv) 〖(0.009)〗^(1/3)Let 𝑦=(𝑥)^(1/3) where 𝑥=0. 008 & ∆𝑥=0. 001 Differentiating w.r.t.𝑥 𝑑𝑦/𝑑𝑥=𝑑(〖𝑥 〗^(1/3) )/𝑑𝑥=1/3 𝑥^((−2)/3)=1/(3〖 𝑥〗^( 2/3) ) Using ∆𝑦=𝑑𝑦/𝑑𝑥 ∆𝑥 ∆𝑦=1/(3〖 𝑥〗^( 2/3) ) ×∆𝑥 Putting Values ∆𝑦=1/(3(0. 008)^( 2/3) ) ×0. 001 ∆𝑦=(0. 001)/(3(8/1000)^(2/3) ) ∆𝑦=(0. 001)/(3(2/10)^( 3 × 2/3) ) ∆𝑦=(0. 001)/(3(2/10)^2 ) ∆𝑦=(0. 001)/(3 × 4/100) ∆𝑦=(0.001 × 100)/12 ∆𝑦=0. 008 We know that ∆𝑦=𝑓(𝑥+∆𝑥)−𝑓(𝑥) ∆𝑦=〖(𝑥+∆𝑥) 〗^(1/3)−〖𝑥 〗^(1/3) Putting Values 0. 008=(0. 008" " +0. 001)^( 1/3)−(0. 008" " )^( 1/3) 0. 008=(0. 009)^( 1/3)−(0. 008)^( 1/3) 0. 008=(0. 009)^( 1/3)−(8/1000)^( 1/3) 0. 008=(0. 009)^( 1/3)−(2/10)^( 3 × 1/3) 0. 008=(0. 009)^( 1/3)−(2/10) 0. 008=(0. 009)^( 1/3)−0. 2 0. 008+0. 2=(0. 009)^( 1/3) (0. 009)^( 1/3)=0. 208 Thus , Approximate Value of (0 . 009)^(1/3) is 𝟎. 𝟐𝟎𝟖

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo