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Q.

If $y = x^{n}$ , then the ratio of relative errors in $y$ and $x,$ is

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a

2 : 1

b

$n : 1$

c

$1 : n$

d

1 : 1

answer is D.

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Detailed Solution

We have,

$\begin{array}{l} y = x^{n} \\ \Rightarrow \log y = n \log x \\ \Rightarrow \frac{1}{y} \frac{d y}{d x} = \frac{n}{x} \Rightarrow \frac{d y}{d x} = \frac{n y}{x} \\ ∴ Δ y = \frac{d y}{d x} Δ x \\ \Rightarrow Δ y = \frac{n y}{x} Δ x \Rightarrow \frac{Δ y}{y} = (\frac{Δ x}{x}) \times n \Rightarrow \frac{Δ y}{y} \div \frac{Δ x}{x} = n \end{array}$

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If y=xn, then the ratio of relative errors in y and x, is