PUC Karnataka Science Class 12Department of Pre-University Education, Karnataka
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Solution for Using Differential, Find the Approximate Value of the ( 82 ) 1 4 ? - PUC Karnataka Science Class 12 - Mathematics

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Question

Using differential, find the approximate value of the $\left( 82 \right)^\frac{1}{4}$ ?

Solution

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

$\text { Let }:$

$x = 81$

$x + ∆ x = 82$

$\text { Then},$

$∆ x = 1$

$\text { For } x = 81,$

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

$\text { Let }:$

$dx = ∆ x = 1$

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

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

$\Rightarrow \left( \frac{dy}{dx} \right)_{x = 81} = \frac{1}{108}$

$\therefore ∆ y = dy = \frac{dy}{dx}dx = \frac{1}{108} \times 1 = 0 . 009259$

$\Rightarrow ∆ y = 0 . 009259$

$\therefore \left( 82 \right)^\frac{1}{4} = y + ∆ y = 3 . 009259$

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Solution Using Differential, Find the Approximate Value of the ( 82 ) 1 4 ? Concept: Approximations.
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