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. (xiv) γ(3.968)γ^(3/2)Let π¦=π₯^( 3/2) where π₯=4 & βπ₯=β0. 032 Now, π¦=π₯^( 3/2) Differentiating w.r.t.π₯ ππ¦/ππ₯=π(π₯^( 3/2) )/ππ₯ ππ¦/ππ₯=3/2 γπ₯ γ^(1/2) Using βπ¦=ππ¦/ππ₯ βπ₯ βπ¦=3/2 π₯^( 1/2) βπ₯ Putting Values βπ¦=3/2 (4)^( 1/2) . (β0. 032) βπ¦=3/2 (2^2 )^( 1/2) . (β0. 032) βπ¦=3/2 Γ 2 Γ (β0. 032) βπ¦=3 Γ (β0. 032) βπ¦=β0. 096 We know that βπ¦=π(π₯+βπ₯)βπ(π₯) So, βπ¦=(π₯+βπ₯)^( 3/2)βπ₯^( 3/2) Putting Values β0. 096=(4+(β0. 032))^( 3/2)β(4)^( 3/2) β0. 096=(4β0. 032)^( 3/2)βγ(2)^2γ^( Γ 3/2) β0. 096=(3. 968)^( 3/2)β2^3 β0. 096=(3. 968)^( 3/2)β8 β0. 096+8=(3. 968)^( 3/2) 7. 904=(3. 968)^( 3/2) (3. 968)^( 3/2)=7.904 Thus, Approximate Values of (3. 968)^( 3/2) is π. πππ