Share

Books Shortlist

Solution for Using Differential, Find the Approximate Value of the ( 17 81 ) 1 4 ? - CBSE (Commerce) Class 12 - Mathematics

Question

Using differential, find the approximate value of the $\left( \frac{17}{81} \right)^\frac{1}{4}$ ?

Solution

$\text { Consider the function } y = f\left( x \right) = \left( x \right)^\frac{1}{4} .$

$\text { Let }:$

$x = \frac{16}{81}$

$x + ∆ x = \frac{17}{81}$

$\text { Then },$

$∆ x = \frac{1}{81}$

$\text { For } x = \frac{16}{81},$

$y = \left( \frac{16}{81} \right)^\frac{1}{4} = \frac{2}{3}$

$\text { Let }:$

$dx = ∆ x = \frac{1}{81}$

$\text { Now }, y = \left( x \right)^\frac{1}{4}$

$\Rightarrow \frac{dy}{dx} = \frac{1}{4 \left( x \right)^\frac{3}{4}}$

$\Rightarrow \left( \frac{dy}{dx} \right)_{x = \frac{16}{81}} = \frac{27}{32}$

$\therefore ∆ y = dy = \frac{dy}{dx}dx = \frac{27}{32} \times \frac{1}{81} = \frac{1}{96} = 0 . 01042$

$\Rightarrow ∆ y = 0 . 01042$

$\therefore \left( \frac{17}{81} \right)^\frac{1}{4} = y + ∆ y = 0 . 6771$

Is there an error in this question or solution?

Video TutorialsVIEW ALL [2]

Solution Using Differential, Find the Approximate Value of the ( 17 81 ) 1 4 ? Concept: Approximations.
S