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

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(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.

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