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. (vi) 〖(15)〗^(1/4)Let 𝑦=〖𝑥 〗^(1/4) where 𝑥=16 , ∆𝑥=−1 Now, 𝑦=𝑥^( 1/4) Differentiating w.r.t.𝑥 𝑑𝑦/𝑑𝑥=𝑑(𝑥^( 1/4) )/𝑑𝑥=1/4 𝑥^( (1 − 4)/4 )=1/4 𝑥^( (−3)/( 4) ) Using ∆𝑦=𝑑𝑦/𝑑𝑥 ∆𝑥 ∆𝑦=1/(4(𝑥)^( 3/4) ) ∆𝑥 Putting Values ∆𝑦=1/(4(16)^( 3/4) ) . (−1) ∆𝑦=1/(4(2^4 )^( 3/4) ) (−1) ∆𝑦=(−1)/(4 × 2^3 ) ∆𝑦=(−1)/(4 × 8) ∆𝑦=(−1)/32 ∆𝑦=−0. 03125 We know that ∆𝑦=𝑓(𝑥+∆𝑥)−𝑓(𝑥) ∆𝑦=(𝑥+∆𝑥)^(1/4)−(𝑥)^(1/4) Putting Values −0. 03125=(16+(−1))^( 1/4)−〖(16) 〗^(1/4) −0. 03125=(16−1)^( 1/4)−(2)^(4 × 1/4) −0. 03125=(15)^( 1/4)−2 −0. 03125+2=(15)^( 1/4) −0. 03125+2=(15)^( 1/4) 1. 96875=(15)^( 1/4) Thus, Approximate Value of (15)^( 1/4) is 𝟏. 𝟗𝟔𝟖𝟕𝟓

#### 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.