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# If y = xn, then the ratio of relative errors in y and x is - CBSE (Science) Class 12 - Mathematics

#### Question

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

• 1 : 1

• 2 : 1

• 1 : n

• n : 1

#### Solution

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 Concept: Approximations.
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