Check sibling questions

Ex 6.4, 1 (v) - Find approximate value of (0.999)^1/10 (STEP-by-STEP)

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

Get Real time Doubt solving from 8pm to 12 am!


Transcript

Ex 6.4, 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

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.