Using differentials, find the approximate value of each of the following up to 3 places of decimal.
pranitapathak00:
1o th
Answers
Answered by
1
Answer:
Let y=x13
Let x=0.008
dx=0.001
So that x+dx=0.009
Now (x+Δx)13−x13
⇒(0.009)13−(0.008)13
⇒(0.009)13−0.2
∴(0.009)13−0.2+Δy-----(1)
Step 2:
Also dydxΔx is approximately equal to dy
dy=(dydx)Δx
=13x23Δx
=13(0.008)23×0.001
=13(0.2)2×0.001
=0.0013×0.04
=0.0010.12
=1120
=0.008
Step 3:
Approximate value of Δy=dy=0.008
Hence from Equation(1) we have
(0.009)13=0.2+0.008
=0.208
Similar questions