Check Full Chapter Explained - Continuity and Differentiability - Application of Derivatives (AOD) Class 12

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

Transcript

Ex 6.4, 1 Using differentials, find the approximate value of each of the following up to 3 places of decimal. (i) √25.3 Let y = √π‘₯ where x = 25 & β–³ x = 0.3 Since y = √π‘₯ 𝑑𝑦/𝑑π‘₯ = (𝑑(√π‘₯))/𝑑π‘₯ = 1/(2√π‘₯) Now, βˆ†π‘¦ = 𝑑𝑦/𝑑π‘₯ β–³x = 1/(2√π‘₯) (0.3) = 1/(2√25) (0.3) = 1/(2 Γ— 5) Γ— 0.3 = 0.3/10 = 0.03 Also, βˆ†π‘¦=𝑓(π‘₯+βˆ†π‘₯)βˆ’π‘“(π‘₯) Putting values βˆ†π‘¦=√(π‘₯+βˆ†π‘₯)βˆ’βˆšπ‘₯ 0. 03=√(25+0. 3)βˆ’βˆš25 0. 03=√(25. 3)βˆ’5 0. 03+5=√(25. 3) √(25. 3)=5. 03 Hence, approximate value of √25.3 is 5.03

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.