# Ex 6.4, 1 (ix) - Chapter 6 Class 12 Application of Derivatives (Term 1)

Last updated at April 15, 2021 by Teachoo

Last updated at April 15, 2021 by Teachoo

Transcript

Ex 6.4, 1 Using differentials, find the approximate value of each of the following up to 3 places of decimal. (ix) ใ(82)ใ^(1/4)Let ๐ฆ=(๐ฅ)^( 1/4) where ๐ฅ=81 โ๐ฅ=1 Now, ๐ฆ=(๐ฅ)^( 1/4) Differentiating w.r.t.๐ฅ ๐๐ฆ/๐๐ฅ=๐(๐ฅ^( 1/4) )/๐๐ฅ=1/4 ใ๐ฅ ใ^(1/4 โ 1)=1/4 ใ๐ฅ ใ^((โ3)/( 4))=1/(4ใ๐ฅ ใ^(3/4) ) Using โ๐ฆ=๐๐ฆ/๐๐ฅ โ๐ฅ โ๐ฆ=1/(4ใ ๐ฅ ใ^(3/4) ) โ๐ฆ Putting Values โ๐ฆ=1/(4(81)^( 3/4) ) ร (1) โ๐ฆ=1/(4 ร3^(4 ร 3/4 ) ) ร (1) โ๐ฆ=1/(4 ร 3^3 ) โ๐ฆ=1/(4 ร27) โ๐ฆ=1/108 โ๐ฆ=0. 009 We know that โ๐ฆ=๐(๐ฅ+โ๐ฅ)โ๐(๐ฅ) So, โ๐ฆ=(๐ฅ+โ๐ฅ)^( 1/4) โ(๐ฅ)^( 1/4) Putting Values 0. 009=(81+1)^( 1/4)โใ(81) ใ^(1/4) 0. 009=(82)^( 1/4)โ(3)^(4 ร 1/4 ) 0. 009=(82)^( 1/4)โ3 0. 009+3=(82)^( 1/4) 3. 009=(82)^( 1/4) Thus, the Approximate Value of (82)^( 1/4) is ๐. ๐๐๐

Ex 6.4

Ex 6.4, 1 (i)
Important
Deleted for CBSE Board 2022 Exams

Ex 6.4, 1 (ii) Deleted for CBSE Board 2022 Exams

Ex 6.4, 1 (iii) Deleted for CBSE Board 2022 Exams

Ex 6.4, 1 (iv) Deleted for CBSE Board 2022 Exams

Ex 6.4, 1 (v) Important Deleted for CBSE Board 2022 Exams

Ex 6.4, 1 (vi) Deleted for CBSE Board 2022 Exams

Ex 6.4, 1 (vii) Deleted for CBSE Board 2022 Exams

Ex 6.4, 1 (viii) Deleted for CBSE Board 2022 Exams

Ex 6.4, 1 (ix) Deleted for CBSE Board 2022 Exams You are here

Ex 6.4, 1 (x) Deleted for CBSE Board 2022 Exams

Ex 6.4, 1 (xi) Important Deleted for CBSE Board 2022 Exams

Ex 6.4, 1 (xii) Deleted for CBSE Board 2022 Exams

Ex 6.4, 1 (xiii) Deleted for CBSE Board 2022 Exams

Ex 6.4, 1 (xiv) Important Deleted for CBSE Board 2022 Exams

Ex 6.4, 1 (xv) Deleted for CBSE Board 2022 Exams

Ex 6.4,2 Deleted for CBSE Board 2022 Exams

Ex 6.4,3 Important Deleted for CBSE Board 2022 Exams

Ex 6.4,4 Deleted for CBSE Board 2022 Exams

Ex 6.4,5 Important Deleted for CBSE Board 2022 Exams

Ex 6.4,6 Deleted for CBSE Board 2022 Exams

Ex 6.4,7 Deleted for CBSE Board 2022 Exams

Ex 6.4,8 (MCQ) Important Deleted for CBSE Board 2022 Exams

Ex 6.4,9 (MCQ) Deleted for CBSE Board 2022 Exams

About the Author

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.