Check sibling questions

Ex 6.4, 1 (vi) - Find approximate value of (15)^1/4 (upto 3 decimals)

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


Transcript

Ex 6.4, 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's photo - Co-founder, Teachoo

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.