1.

The value of `(127)^(1//3)` to four decimal places, isA. `5.0267`B. `5.4267`C. `5.5267`D. `5.001`

Answer» Correct Answer - A
Let `y=x^(1//3), x=125 and x+ Delta x =127`. Then,
`dy/dx=1/(3x^(2//3)) Delta x = 2`
When, x =125, we have
`y=5 and dy/dx=1/75`
`:." "Deltay=dy/dx Deltax rArr Deltay= 1/75 xx2=2/75`
`:." "(127)^(1//3) = y+ Deltay=5+2/75=5+8/3 xx1/100`
`rArr" "(127)^(1//3) = 5+(2.6667)/100=5.02667 cong 5.0267`


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