Approximations (using Differentiation)

Finding rate of change →
Chapter 6 Class 12 Application of Derivatives
Serial order wise

Question 1 (iii) - Approximations (using Differentiation) - Chapter 6 Class 12 Application of Derivatives

Last updated at May 29, 2023 by

Ex 6.4, 1 (iii) - Find approximate value upto 3 decimal places √0.6

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

Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class

Book a free demo

Transcript

Question 1 Using differentials, find the approximate value of each of the following up to 3 places of decimal. (iii) √0.6 Let y = √𝑥 where x = 0.64 & △x = –0.04 Since y = √𝑥 𝑑𝑦/𝑑𝑥 = (𝑑(√𝑥))/𝑑𝑥 = 1/(2√𝑥) Now, ∆𝑦 = 𝑑𝑦/𝑑𝑥 △x = 1/(2√0.64) (–0.04) = 1/(2√(64/100)) (–0.04) = 1/(2 ×8/10) × (–0.04) = (−10 × 0.04)/16 = (−10 × 4)/(16 × 100) = –0.025 Also, ∆𝑦=𝑓(𝑥+∆𝑥)−𝑓(𝑥) Putting values ∆𝑦=√(𝑥+∆𝑥)−√𝑥 −0. 025=√(0.64−0.04)−√0.64 −0.025=√0.60−0.8 0.8 – 0. 025=√0.60 √0.60=0.775 Hence, approximate value of √0.60 is 0.775

Ask a doubt
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 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.