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Chapter 6 Class 12 Application of Derivatives
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Ex 6.4, 1 (xiv) - Find approximate value of (3.968)^1/2 - Teachoo

Ex 6.4, 1 (xiv) - Chapter 6 Class 12 Application of Derivatives - Part 2
Ex 6.4, 1 (xiv) - Chapter 6 Class 12 Application of Derivatives - Part 3

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Question 1 Using differentials, find the approximate value of each of the following up to 3 places of decimal. (xiv) γ€–(3.968)γ€—^(3/2)Let 𝑦=π‘₯^( 3/2) where π‘₯=4 & βˆ†π‘₯=βˆ’0. 032 Now, 𝑦=π‘₯^( 3/2) Differentiating w.r.t.π‘₯ 𝑑𝑦/𝑑π‘₯=𝑑(π‘₯^( 3/2) )/𝑑π‘₯ 𝑑𝑦/𝑑π‘₯=3/2 γ€–π‘₯ γ€—^(1/2) Using βˆ†π‘¦=𝑑𝑦/𝑑π‘₯ βˆ†π‘₯ βˆ†π‘¦=3/2 π‘₯^( 1/2) βˆ†π‘₯ Putting Values βˆ†π‘¦=3/2 (4)^( 1/2) . (βˆ’0. 032) βˆ†π‘¦=3/2 (2^2 )^( 1/2) . (βˆ’0. 032) βˆ†π‘¦=3/2 Γ— 2 Γ— (βˆ’0. 032) βˆ†π‘¦=3 Γ— (βˆ’0. 032) βˆ†π‘¦=βˆ’0. 096 We know that βˆ†π‘¦=𝑓(π‘₯+βˆ†π‘₯)βˆ’π‘“(π‘₯) So, βˆ†π‘¦=(π‘₯+βˆ†π‘₯)^( 3/2)βˆ’π‘₯^( 3/2) Putting Values βˆ’0. 096=(4+(βˆ’0. 032))^( 3/2)βˆ’(4)^( 3/2) βˆ’0. 096=(4βˆ’0. 032)^( 3/2)βˆ’γ€–(2)^2γ€—^( Γ— 3/2) βˆ’0. 096=(3. 968)^( 3/2)βˆ’2^3 βˆ’0. 096=(3. 968)^( 3/2)βˆ’8 βˆ’0. 096+8=(3. 968)^( 3/2) 7. 904=(3. 968)^( 3/2) (3. 968)^( 3/2)=7.904 Thus, Approximate Values of (3. 968)^( 3/2) is πŸ•. πŸ—πŸŽπŸ’

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.