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Solution for If Y = Xn, Then the Ratio of Relative Errors in Y and X is (A) 1 : 1 (B) 2 : 1 (C) 1 : N (D) N : 1 - CBSE (Commerce) Class 12 - Mathematics

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Question

If y = xn, then the ratio of relative errors in y and x is
(a) 1 : 1
(b) 2 : 1
(c) 1 : n
(d) n : 1

Solution

(d) n : 1

\[\text { Let } \frac{∆ x}{x} \text { be the relative error in x and} \frac{∆ y}{y} \text { be the error in y } . \]

\[\text { Now,} y = x^n \]

\[ \Rightarrow \frac{dy}{dx} = n x^{n - 1} \]

\[ \Rightarrow \frac{∆ y}{y} = \frac{n x^{n - 1}}{y}dx\]

\[ \Rightarrow \frac{∆ y}{y} = \frac{n x^{n - 1}}{x^n}dx = n\frac{∆ x}{x}\]

\[ \Rightarrow \frac{∆ y}{y}: \frac{∆ x}{x} = n: 1\]

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Solution If Y = Xn, Then the Ratio of Relative Errors in Y and X is (A) 1 : 1 (B) 2 : 1 (C) 1 : N (D) N : 1 Concept: Approximations.
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