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Ex 6.4, 1 (xiii) - Find approximate value upto 3 decimals - (81.5)^1/4

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

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Ex 6.4, 1 Using differentials, find the approximate value of each of the following up to 3 places of decimal. (xiii) 〖(81.5)〗^(1/4)Let 𝑦=(𝑥)^( 1/4) where 𝑥=81 & ∆𝑥=0. 5 Now, 𝑦=𝑥^( 1/4) Differentiating w.r.t.𝑥 𝑑𝑦/𝑑𝑥=𝑑(𝑥^( 1/4) )/𝑑𝑥=1/4 𝑥^( 1/4 − 1)=1/4 𝑥^( (− 3)/( 4)) =1/(4𝑥^(3/4) ) ∆ 𝑥 Using ∆𝑦=𝑑𝑦/𝑑𝑥 ∆𝑥 ∆𝑦=𝑑𝑦/(4𝑥^(3/4) ) ∆𝑥 Putting Values ∆𝑦=1/(4(81)^( 3/4) ) × (0. 5) ∆𝑦=(0. 5)/(4 × (3^( 4) )^( 3/4) ) ∆𝑦=(0. 5)/(4 × 3^( 3) ) ∆𝑦=(0. 5)/(4 × 27) ∆𝑦=(0. 5)/108 ∆𝑦=0. 0046 We know that ∆𝑦=𝑓(𝑥+∆𝑥)−𝑓(𝑥) So, ∆𝑦=(𝑥+∆𝑥)^( 1/4)−𝑥^( 1/4) Putting Values 0. 0046=(81+0. 5)^( 1/4)−(81)^( 1/4) 0. 0046=(81. 5)^( 1/4)−(3^4 )^( 1/4) 0. 0046=(81. 5)^( 1/4)−3 0. 0046+3=(81. 5)^( 1/4) 3. 0046=(81. 5)^( 1/4) Thus, Approximate Value of (81. 5)^( 1/4) is 𝟑. 𝟎𝟎𝟒𝟔

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.