Approximations (using Differentiation)

Chapter 6 Class 12 Application of Derivatives
Serial order wise

Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class

### Transcript

Question 1 Using differentials, find the approximate value of each of the following up to 3 places of decimal. (ix) γ(82)γ^(1/4)Let π¦=(π₯)^( 1/4) where π₯=81 βπ₯=1 Now, π¦=(π₯)^( 1/4) Differentiating w.r.t.π₯ ππ¦/ππ₯=π(π₯^( 1/4) )/ππ₯=1/4 γπ₯ γ^(1/4 β 1)=1/4 γπ₯ γ^((β3)/( 4))=1/(4γπ₯ γ^(3/4) ) Using βπ¦=ππ¦/ππ₯ βπ₯ βπ¦=1/(4γ π₯ γ^(3/4) ) βπ¦ Putting Values βπ¦=1/(4(81)^( 3/4) ) Γ (1) βπ¦=1/(4 Γ3^(4 Γ 3/4 ) ) Γ (1) βπ¦=1/(4 Γ 3^3 ) βπ¦=1/(4 Γ27) βπ¦=1/108 βπ¦=0. 009 We know that βπ¦=π(π₯+βπ₯)βπ(π₯) So, βπ¦=(π₯+βπ₯)^( 1/4) β(π₯)^( 1/4) Putting Values 0. 009=(81+1)^( 1/4)βγ(81) γ^(1/4) 0. 009=(82)^( 1/4)β(3)^(4 Γ 1/4 ) 0. 009=(82)^( 1/4)β3 0. 009+3=(82)^( 1/4) 3. 009=(82)^( 1/4) Thus, the Approximate Value of (82)^( 1/4) is π. πππ