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:

We have,

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

JEE Main 2023 Question Papers with Solutions

JEE Main 2024 Syllabus

Best Books for JEE Main 2024

JEE Advanced 2024: Exam date, Syllabus, Eligibility Criteria

JEE Main 2024: Exam dates, Syllabus, Eligibility Criteria

JEE 2024: Exam Date, Syllabus, Eligibility Criteria

NCERT Solutions For Class 6 Maths Data Handling Exercise 9.3

JEE Crash Course – JEE Crash Course 2023

NEET Crash Course – NEET Crash Course 2023

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

Solution:

Related content