Find the value of (127)^{1/3} up to four deci | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Let $y = x^{1/3}$,where $x = 125$ and $x + \Delta x = 127$. Then $\Delta x = 2$. The derivative is $\frac{dy}{dx} = \frac{1}{3x^{2/3}}$. For $x =

Vedclass · Accepted Answer

$5.0267$

Vedclass · Answer

(A) Let $y = x^{1/3}$,where $x = 125$ and $x + \Delta x = 127$. Then $\Delta x = 2$. The derivative is $\frac{dy}{dx} = \frac{1}{3x^{2/3}}$. For $x = 125$,$y = (125)^{1/3} = 5$ and $\frac{dy}{dx} = \frac{1}{3(125)^{2/3}} = \frac{1}{3(25)} = \frac{1}{75}$. Using the approximation $\Delta y \approx \frac{dy}{dx} \cdot \Delta x$,we get $\Delta y \approx \frac{1}{75} 	imes 2 = \frac{2}{75} = 0.02666... \approx 0.0267$. Therefore,$(127)^{1/3} = y + \Delta y = 5 + 0.0267 = 5.0267$.

Find the value of $(127)^{1/3}$ up to four decimal places.

Similar Questions

What is the value of $\sqrt[3]{26}$ corrected up to three decimal places?

The approximate value of $\sqrt[3]{64.04}$ is

The nearest approximate value of $\sqrt{2023}$ is

The approximate value of $(3.978)^{\frac{3}{2}}$ is

There is a possible error of $0.02 \ cm$ in measuring the base diameter of a right circular cone as $14 \ cm$. If the semi-vertical angle of the cone is $45^{\circ}$,then the approximate error in its volume is (in $cm^3$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module