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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.

You can download the question paper hereΒ  https://www.teachoo.com/cbse/sample-papers/


Find approximate change in value of 1/x^2, when x changes from 2 to

Question 8 - CBSE Class 12 Sample Paper for 2018 Boards - Part 2


Transcript

Question 8 Find the approximate change in the value of 1/π‘₯^2 , when x changes from x = 2 to x = 2.002 Let y = 1/π‘₯^2 We need to find change in value of y when x changes from 2 to 0.002 ∴ βˆ†x = 2.002 – 2 = 0.002 We need to find βˆ†y Now, βˆ†y = 𝑑𝑦/𝑑π‘₯ βˆ†x βˆ†y = 𝑑(1/π‘₯^2 )/𝑑π‘₯ βˆ†x βˆ†y = 𝑑(π‘₯^(βˆ’2) )/𝑑π‘₯ Γ— 0.002 βˆ†y = –2 Γ— x–3 Γ— 0.002 Since we go from x = 2 to x = 2.002 We put x = 2 in βˆ†y βˆ†y = –2 Γ— 2–3 Γ— 0.002 βˆ†y = –2 Γ— 1/2^3 Γ— 0.002 βˆ†y = –2 Γ— 1/2^3 Γ— 2/1000 βˆ†y = (βˆ’1)/2000 βˆ†y = – 0.0005 ∴ 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 12 years. He provides courses for Maths and Science at Teachoo.