CBSE (Science) Class 12CBSE
Share
Notifications

View all notifications
Books Shortlist
Your shortlist is empty

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

Login
Create free account


      Forgot password?

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

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

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

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

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

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

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

  Is there an error in this question or solution?

APPEARS IN

Video TutorialsVIEW ALL [2]

Solution If y = xn, then the ratio of relative errors in y and x is Concept: Approximations.
S
View in app×