Chapter 6 Class 12 Application of Derivatives
Serial order wise

Ex 6.4, 1 (xii) - Find approximate value upto 3 decimals - (26.57)^1/3

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

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Transcript

Question 1 Using differentials, find the approximate value of each of the following up to 3 places of decimal. (xii) 〖(26.57)〗^(1/3)Let 𝑦=𝑥^( 1/3) where 𝑥=27 & ∆ 𝑥=−0. 43 Now, 𝑦=𝑥^( 1/3) Differentiating w.r.t.𝑥 𝑑𝑦/𝑑𝑥=𝑑(𝑥^( 1/3) )/𝑑𝑥=1/3 𝑥^( 1/3 − 1)=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 (27)^( 2/( 3)) ) × (−0. 43) ∆𝑦=(−0. 43)/(3 × 3^(3 × 2/( 3)) ) ∆𝑦=(−0. 43)/(3 × 3^2 ) ∆𝑦=(−0. 43)/(3 × 9) ∆𝑦=(−0. 43)/27 ∆𝑦=−0. 015926 We know that ∆𝑦=𝑓(𝑥+∆𝑥)−𝑓(𝑥) So, ∆𝑦=〖(𝑥+∆𝑥) 〗^(1/3)−𝑥^( 1/3) Putting Values −0. 015926=(27+(−0. 43))^( 1/3)−(27)^( 1/3) −0. 015926=(26. 57)^( 1/3)−(27)^( 3 × 1/3) −0. 015926=(26. 57)^( 1/3)−3 −0. 015926+3=(26. 53)^( 1/3) 2. 984=(26. 53)^( 1/3) Thus, the Approximate Values of (26. 53)^( 1/3) is 𝟐. 𝟗𝟖𝟒

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.