Question

Find the approximate value of (127)^1/3.

(a) 5.0267

(b) 2.0267

(c) 8.0267

(d) 5.04

I have been asked this question by my college director while I was bunking the class.

I would like to ask this question from Derivatives Application topic in chapter Application of Derivatives of Mathematics – Class 12

Answer 1

Correct option is (a) 5.0267

For explanation: Let y=(x)^1/3. Let x=125 and Δx=2

Then, Δy=(x+Δx)^1/3-x^1/3

Δy=(127)^1/3-(125)^1/3

(127)^1/3=Δy+5

dy is approximately equal to Δy is equal to

dy=\(\frac{dy}{dx}\)Δx

dy=\(\frac{1}{3x^{2/3}}\).Δx

dy=\(\frac{1}{3×125^{2/3}} (2)\)

dy=2/75=0.0267

∴ The approximate value of (127)^1/3 is 5+0.0267=5.0267