If y = x4 – 10 and if x changes from 2 to 1.99, what is the change in y

(A)0.32   (B) 0.032   (C) 5.68   (D) 5.968

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  1. Chapter 6 Class 12 Application of Derivatives (Term 1)
  2. Serial order wise

Transcript

Question 11 If y = x4 โ€“ 10 and if x changes from 2 to 1.99, what is the change in y 0.32 (B) 0.032 (C) 5.68 (D) 5.968 Since, ๐‘ฅ changes from 2 to 1.99 So, โˆ†๐’™ = ๐’™_๐Ÿโˆ’๐’™_๐Ÿ = 1.99 โˆ’ 2 โˆ† ๐‘ฅ = โˆ’ 0.01 Finding ๐’…๐’š/๐’…๐’™ ๐‘ฆ=๐‘ฅ^4โˆ’10 ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ = 4๐’™^๐Ÿ‘ Putting ๐ฑ=๐Ÿ, as value of ๐‘ฅ changes from 2 ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ= 4(2)^3 ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ=๐Ÿ‘๐Ÿ Now, โˆ†๐’š = ๐’…๐’š/๐’…๐’™ โˆ†๐’™ Putting values of โˆ†๐‘ฅ = 0.01 and ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ = 32 โˆ†๐‘ฆ = 32 (โˆ’0.01) โˆ†๐’š = 0.32 โˆด Approximate change in ๐‘ฆ is 0.32 So, the correct answer is (A)

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Davneet Singh
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.