Approximations (using Differentiation)

Chapter 6 Class 12 Application of Derivatives
Serial order wise

### Transcript

Question 1 Using differentials, find the approximate value of each of the following up to 3 places of decimal. (v) 〖(0.999)〗^(1/10)Let 𝑦=〖𝑥 〗^(1/10) where 𝑥=1 , ∆𝑥=−0. 001 Now, 𝑦=𝑥^( 1/10) Differentiating w.r.t.𝑥 𝑑𝑦/𝑑𝑥=𝑑(𝑥^( 1/10) )/𝑑𝑥=1/10 𝑥^((−9)/10)=1/(10〖 𝑥〗^(9/10) ) Using ∆𝑦=𝑑𝑦/𝑑𝑥 ∆𝑥 Putting Values ∆𝑦= 1/(10〖 𝑥〗^(9/10) ) ∆𝑥 ∆𝑦= 1/(10 (1)^(9/10) ) × (−0. 001) ∆𝑦= 1/10 ×(−0. 001) ∆𝑦=−0. 0001 We know that ∆𝑦=𝑓(𝑥+∆𝑥)−𝑓(𝑥) ∆𝑦=〖(𝑥+∆𝑥) 〗^(1/10)−𝑥^( 1/10) Putting Values ∆𝑦=(1+(−0. 001))^(1/10)−(1)^(1/10) −0. 0001=(0. 999)^(1/10)−1 −0. 0001+1=(0. 999)^(1/10) 0. 9999=(0. 999)^(1/10) Thus, the Approximate Value of (0. 999)^(1/10) is 𝟎. 𝟗𝟗𝟗𝟗

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#### Davneet Singh

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, Social Science, Physics, Chemistry, Computer Science at Teachoo.