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# Solution for Using Differential, Find the Approximate Value of the ( 15 ) 1 4 ? - CBSE (Science) Class 12 - Mathematics

#### Question

Using differential, find the approximate value of the $\left( 15 \right)^\frac{1}{4}$ ?

#### Solution

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

$\text{ Let }:$

$x = 16$

$x + ∆ x = 15$

$\text { Then },$

$∆ x = - 1$

$\text { For } x = 16,$

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

$\text { Let }:$

$dx = ∆ x = - 1$

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

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

$\Rightarrow \left( \frac{dy}{dx} \right)_{x = 16} = \frac{1}{32}$

$\therefore ∆ y = dy = \frac{dy}{dx}dx = \frac{1}{32} \times \left( - 1 \right) = \frac{- 1}{32}$

$\Rightarrow ∆ y = \frac{- 1}{32} = - 0 . 03125$

$\therefore \left( 15 \right)^\frac{1}{4} = y + ∆ y = 1 . 96875$

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Solution Using Differential, Find the Approximate Value of the ( 15 ) 1 4 ? Concept: Approximations.
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