Question 8
Find the approximate change in the value of 1/๐ฅ^2 , when x changes from x = 2 to x = 2.002
Let y = 1/๐ฅ^2
We need to find change in value of y when x changes from 2 to 0.002
โด โx = 2.002 โ 2 = 0.002
We need to find โy
Now,
โy = ๐๐ฆ/๐๐ฅ โx
โy = ๐(1/๐ฅ^2 )/๐๐ฅ โx
โy = ๐(๐ฅ^(โ2) )/๐๐ฅ ร 0.002
โy = โ2 ร xโ3 ร 0.002
Since we go from x = 2 to x = 2.002
We put x = 2 in โy
โy = โ2 ร 2โ3 ร 0.002
โy = โ2 ร 1/2^3 ร 0.002
โy = โ2 ร 1/2^3 ร 2/1000
โy = (โ1)/2000
โy = โ 0.0005
โด y decreases by 0.0005

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.