Miscellaneous

Chapter 6 Class 12 Application of Derivatives
Serial order wise

### Transcript

Misc 1 Using differentials, find the approximate value of each of the following: (a) (17/81)^(1/4) (17/81)^(1/4) = (17)^(1/4)/(81)^(1/4) = (17)^(1/4)/3 Let 𝑦 =𝑥^(1/4) Where 𝑥=16 and △𝑥=1 Since 𝒚 =𝒙^(𝟏/𝟒) 𝑑𝑦/𝑑𝑥=𝑑(𝑥^(1/4) )/𝑑𝑥 = 1/4 𝑥^(1/4 − 1) = 1/4 𝑥^((−3)/4) = 1/(4𝑥^(3/4) ) Now, ∆𝒚=𝒅𝒚/𝒅𝒙 ∆𝒙 ∆𝑦 = (1/(4𝑥^(3/4) ))∆𝑥 Putting values ∆𝑦 = 1/4 × 1/(16)^(3/4) × 1 = 1/4 × 1/(2^4 )^(3/4) = 1/4 × 1/2^3 = 𝟏/𝟑𝟐 Now, (17)^(1/4)=𝑦+∆𝑦 Putting values (17)^(1/4) = (16)^(1/4)+∆𝑦 (17)^(1/4) = (2^4 )^(1/4)+∆𝑦 (17)^(1/4) = 2+∆𝑦 (17)^(1/4) = 2 + 1/32 (17)^(1/4) = 2+ 0.03125 (𝟏𝟕)^(𝟏/𝟒) = 2.03125 Now, Approximate value of (𝟏𝟕/𝟖𝟏)^(𝟏/𝟒) = (17)^(1/4)/3 = 2.03125/3 = 0.677 Hence, approximate value of (17/81)^(1/4) is 0.677 (As approximate value of (17)^(1/4) = 2.03125)

#### Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.