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प्रश्न
Using differential, find the approximate value of the \[\sqrt{0 . 082}\] ?
बेरीज
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उत्तर
\[\text { Consider the function } y = f\left( x \right) = \sqrt{x} . \]
\[\text { Let }: \]
\[x = 0 . 0841\]
\[x + ∆ x = 0 . 082\]
\[\text { Then }, \]
\[ ∆ x = - 0 . 0021\]
\[\text { For } x = 0 . 0841, \]
\[ y = \sqrt{0 . 0841} = 0 . 29\]
\[\text { Let }: \]
\[ dx = ∆ x = - 0 . 0021\]
\[\text { Now,} y = \left( x \right)^\frac{1}{2} \]
\[ \Rightarrow \frac{dy}{dx} = \frac{1}{2\sqrt{x}}\]
\[ \Rightarrow \left( \frac{dy}{dx} \right)_{x = 0 . 0841} = \frac{1}{0 . 58} = \frac{50}{29}\]
\[ \therefore ∆ y = dy = \frac{dy}{dx}dx = \frac{50}{29} \times \left( - 0 . 0021 \right) = - 0 . 0036\]
\[ \Rightarrow ∆ y = - 0 . 0036\]
\[ \therefore \sqrt{0 . 082} = y + ∆ y = 0 . 2864\]
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