The approximate value of sqrt[3]{64.04} is | vedclass

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

Question

(C) Let $f(x) = x^{1/3}$. We need to find the approximate value of $f(64.04)$.Let $x = 64$ and $\Delta x = 0.04$.Then $f(x + \Delta x) \approx f(x) +

Vedclass · Accepted Answer

$4.00083$

Vedclass · Answer

(C) Let $f(x) = x^{1/3}$. We need to find the approximate value of $f(64.04)$.Let $x = 64$ and $\Delta x = 0.04$.Then $f(x + \Delta x) \approx f(x) + f'(x) \cdot \Delta x$.Here,$f(x) = x^{1/3}$,so $f'(x) = \frac{1}{3} x^{-2/3} = \frac{1}{3(x^{1/3})^2}$.For $x = 64$,$f(64) = 64^{1/3} = 4$.$f'(64) = \frac{1}{3(4)^2} = \frac{1}{3 \cdot 16} = \frac{1}{48}$.Now,$f(64.04) \approx 4 + \frac{1}{48} \cdot 0.04$.$f(64.04) \approx 4 + \frac{0.04}{48} = 4 + \frac{4}{4800} = 4 + \frac{1}{1200}$.$f(64.04) \approx 4 + 0.000833...$Thus,the approximate value is $4.00083$.

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

Similar Questions

The diameter of a sphere is measured as $42 \text{ cm}$. If there is an error of $1/77 \text{ cm}$ in measuring it, then the error involved in the volume of that sphere (in cubic centimeters) is

Find the approximate value of $(26.57)^{\frac{1}{3}}$.

The approximate value of $\sin 31^{\circ}$ is

The approximate value of $\frac{1}{(2.002)^2}$ is

If the percentage error in the radius of a circle is $3\%$,then the percentage error in its area is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module