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Ex 6.4
Ex 6.4, 1 (ii) Deleted for CBSE Board 2023 Exams
Ex 6.4, 1 (iii) Deleted for CBSE Board 2023 Exams
Ex 6.4, 1 (iv) Deleted for CBSE Board 2023 Exams You are here
Ex 6.4, 1 (v) Important Deleted for CBSE Board 2023 Exams
Ex 6.4, 1 (vi) Deleted for CBSE Board 2023 Exams
Ex 6.4, 1 (vii) Deleted for CBSE Board 2023 Exams
Ex 6.4, 1 (viii) Deleted for CBSE Board 2023 Exams
Ex 6.4, 1 (ix) Deleted for CBSE Board 2023 Exams
Ex 6.4, 1 (x) Deleted for CBSE Board 2023 Exams
Ex 6.4, 1 (xi) Important Deleted for CBSE Board 2023 Exams
Ex 6.4, 1 (xii) Deleted for CBSE Board 2023 Exams
Ex 6.4, 1 (xiii) Deleted for CBSE Board 2023 Exams
Ex 6.4, 1 (xiv) Important Deleted for CBSE Board 2023 Exams
Ex 6.4, 1 (xv) Deleted for CBSE Board 2023 Exams
Ex 6.4,2 Deleted for CBSE Board 2023 Exams
Ex 6.4,3 Important Deleted for CBSE Board 2023 Exams
Ex 6.4,4 Deleted for CBSE Board 2023 Exams
Ex 6.4,5 Important Deleted for CBSE Board 2023 Exams
Ex 6.4,6 Deleted for CBSE Board 2023 Exams
Ex 6.4,7 Deleted for CBSE Board 2023 Exams
Ex 6.4,8 (MCQ) Important Deleted for CBSE Board 2023 Exams
Ex 6.4,9 (MCQ) Deleted for CBSE Board 2023 Exams
Last updated at March 16, 2023 by Teachoo
Ex 6.4, 1 Using differentials, find the approximate value of each of the following up to 3 places of decimal. (iv) 〖(0.009)〗^(1/3)Let 𝑦=(𝑥)^(1/3) where 𝑥=0. 008 & ∆𝑥=0. 001 Differentiating w.r.t.𝑥 𝑑𝑦/𝑑𝑥=𝑑(〖𝑥 〗^(1/3) )/𝑑𝑥=1/3 𝑥^((−2)/3)=1/(3〖 𝑥〗^( 2/3) ) Using ∆𝑦=𝑑𝑦/𝑑𝑥 ∆𝑥 ∆𝑦=1/(3〖 𝑥〗^( 2/3) ) ×∆𝑥 Putting Values ∆𝑦=1/(3(0. 008)^( 2/3) ) ×0. 001 ∆𝑦=(0. 001)/(3(8/1000)^(2/3) ) ∆𝑦=(0. 001)/(3(2/10)^( 3 × 2/3) ) ∆𝑦=(0. 001)/(3(2/10)^2 ) ∆𝑦=(0. 001)/(3 × 4/100) ∆𝑦=(0.001 × 100)/12 ∆𝑦=0. 008 We know that ∆𝑦=𝑓(𝑥+∆𝑥)−𝑓(𝑥) ∆𝑦=〖(𝑥+∆𝑥) 〗^(1/3)−〖𝑥 〗^(1/3) Putting Values 0. 008=(0. 008" " +0. 001)^( 1/3)−(0. 008" " )^( 1/3) 0. 008=(0. 009)^( 1/3)−(0. 008)^( 1/3) 0. 008=(0. 009)^( 1/3)−(8/1000)^( 1/3) 0. 008=(0. 009)^( 1/3)−(2/10)^( 3 × 1/3) 0. 008=(0. 009)^( 1/3)−(2/10) 0. 008=(0. 009)^( 1/3)−0. 2 0. 008+0. 2=(0. 009)^( 1/3) (0. 009)^( 1/3)=0. 208 Thus , Approximate Value of (0 . 009)^(1/3) is 𝟎. 𝟐𝟎𝟖