Find the approximate value of sqrt{0.6} using | vedclass

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

Question

(A) Let $f(x) = \sqrt{x}$. We want to find the approximate value of $f(0.6)$.Choose $x = 0.64$ and $\Delta x = -0.04$,so that $x + \Delta x = 0.6$.Usi

Vedclass · Accepted Answer

$0.774$

Vedclass · Answer

(A) Let $f(x) = \sqrt{x}$. We want to find the approximate value of $f(0.6)$.Choose $x = 0.64$ and $\Delta x = -0.04$,so that $x + \Delta x = 0.6$.Using the formula $f(x + \Delta x) \approx f(x) + f'(x) \Delta x$:$f'(x) = \frac{1}{2\sqrt{x}}$.At $x = 0.64$,$f(0.64) = \sqrt{0.64} = 0.8$.$f'(0.64) = \frac{1}{2\sqrt{0.64}} = \frac{1}{2(0.8)} = \frac{1}{1.6} = 0.625$.Therefore,$f(0.6) \approx 0.8 + (0.625)(-0.04)$.$f(0.6) \approx 0.8 - 0.025 = 0.775$.The closest option is $0.774$.

Find the approximate value of $\sqrt{0.6}$ using differentials.

Similar Questions

Using differentials,find the approximate value of $\sqrt{0.082}$. Let $f(x) = \sqrt{x}$.

For a given function $y=f(x)$, $\delta y$ denotes the actual error in $y$ corresponding to an actual error $\delta x$ in $x$, and $dy$ denotes the approximate value of $\delta y$. If $y=f(x)=2x^2-3x+4$ and $\delta x=0.02$, then the value of $\delta y - dy$ when $x=5$ is

The approximate value of $\tan ^{-1}(0.999)$ is (use $\pi=3.1415$ )

If $y=2x^3-2x^2+3x-5$, then for $x=2$ and $\Delta x=0.1$, the value of $\Delta y$ is:

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

Vedclass Test Series

Exam Paper Generator

Online Exam Module