Find the approximate change in the value of 1/x 2 , when x changes from x = 2 to x = 2.002

This is a question of CBSE Sample Paper - Class 12 - 2017/18.

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Question 8 Find the approximate change in the value of 1/๐‘ฅ^2 , when x changes from x = 2 to x = 2.002 Let y = 1/๐‘ฅ^2 We need to find change in value of y when x changes from 2 to 0.002 โˆด โˆ†x = 2.002 โ€“ 2 = 0.002 We need to find โˆ†y Now, โˆ†y = ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ โˆ†x โˆ†y = ๐‘‘(1/๐‘ฅ^2 )/๐‘‘๐‘ฅ โˆ†x โˆ†y = ๐‘‘(๐‘ฅ^(โˆ’2) )/๐‘‘๐‘ฅ ร— 0.002 โˆ†y = โ€“2 ร— xโ€“3 ร— 0.002 Since we go from x = 2 to x = 2.002 We put x = 2 in โˆ†y โˆ†y = โ€“2 ร— 2โ€“3 ร— 0.002 โˆ†y = โ€“2 ร— 1/2^3 ร— 0.002 โˆ†y = โ€“2 ร— 1/2^3 ร— 2/1000 โˆ†y = (โˆ’1)/2000 โˆ†y = โ€“ 0.0005 โˆด y decreases by 0.0005

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.