Chapter 6 Class 12 Application of Derivatives
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Ex 6.4, 1 (vii) - Find approximate value of (26)^1/3 - Teachoo

Ex 6.4, 1 (vii) - Chapter 6 Class 12 Application of Derivatives - Part 2
Ex 6.4, 1 (vii) - 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. (vii) 〖(26)〗^(1/3)Let 𝑦=(𝑥)^(1/3) where 𝑥=27 & ∆𝑥=−1 Now, 𝑦=〖𝑥 〗^(1/3) Differentiating w.r.t.𝑥 𝑑𝑦/𝑑𝑥=𝑑(〖𝑥 〗^(1/3) )/𝑑𝑥=1/3 〖𝑥 〗^(1/3 − 1) Using ∆𝑦=𝑑𝑦/𝑑𝑥 ∆𝑥 ∆𝑦=1/(3〖𝑥 〗^(2/( 3) ) ) ∆𝑥 Putting Values ∆𝑦=1/(3(27)^( 2/3 ) )× (−1) ∆𝑦=1/(3(3^3 )^( 2/3 ) )× (−1) ∆𝑦=(−1)/(3〖 × 3〗^(2 ) ) ∆𝑦=(−1)/(3 × 9 ) ∆𝑦=(−1)/27 ∆𝑦=−0. 037037 We know that ∆𝑦=𝑓(𝑥+∆𝑥)−𝑓(𝑥) ∆𝑦=〖(𝑥+∆𝑥) 〗^(1/3)−(𝑥)^( 1/3) Putting Values −0. 037037=〖(27+(−1)) 〗^(1/3)−(27)^( 1/3) −0. 037037=〖(26) 〗^(1/3)−(3)^( 3 × 1/3) −0. 037037=〖(26) 〗^(1/3)−3 −0. 037037+3=〖(26) 〗^(1/3) 2. 9629=〖(26) 〗^(1/3) Thus, Approximate Value of (26)^(1/3) is 𝟐. 𝟗𝟔𝟐𝟗 =1/3 〖𝑥 〗^((− 2)/( 3) )=1/(3〖𝑥 〗^(2/( 3) ) ) ∆𝑦=−0. 037037 We know that ∆𝑦=𝑓(𝑥+∆𝑥)−𝑓(𝑥) ∆𝑦=〖(𝑥+∆𝑥) 〗^(1/3)−(𝑥)^( 1/3) Putting Values −0. 037037=〖(27+(−1)) 〗^(1/3)−(27)^( 1/3) −0. 037037=〖(26) 〗^(1/3)−(3)^( 3 × 1/3) −0. 037037=〖(26) 〗^(1/3)−3 −0. 037037+3=〖(26) 〗^(1/3) 2. 9629=〖(26) 〗^(1/3) Thus, Approximate Value of (26)^(1/3) is 𝟐. 𝟗𝟔𝟐𝟗

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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.