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Solution for Using Differential, Find the Approximate Value of the ( 66 ) 1 3 ? - CBSE (Commerce) Class 12 - Mathematics

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Question

Using differential, find the approximate value of the \[\left( 66 \right)^\frac{1}{3}\] ?

Solution

\[\text { Consider  the  function }  y = f\left( x \right) =  \left( x \right)^\frac{1}{3}  . \] 
\[\text { Let }: \] 
\[  x   = 64  \] 
\[x +  ∆ x = 66\] 
\[\text { Then },   \] 
 
\[ ∆ x = 2\] 
\[\text { For }  x = 64, \] 
\[  y =  \left( 64 \right)^\frac{1}{3}  = 4\] 
\[\text{ Let }: \] 
\[  dx =  ∆ x = 2\] 
\[\text { Now },   y =  \left( x \right)^\frac{1}{3} \] 
\[ \Rightarrow \frac{dy}{dx} = \frac{1}{3 \left( x \right)^\frac{2}{3}}\] 
\[ \Rightarrow  \left( \frac{dy}{dx} \right)_{x = 64}  = \frac{1}{48}\] 
\[ \therefore    ∆ y = dy = \frac{dy}{dx}dx = \frac{1}{48} \times 2 = 0 . 042\] 
\[ \Rightarrow  ∆ y = 0 . 042\] 
\[ \therefore    \left( 66 \right)^\frac{1}{3}  = y +  ∆ y = 4 . 042\]
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APPEARS IN

 RD Sharma Mathematics for Class 12 by R D Sharma (Set of 2 Volume) (2018-19 Session) (with solutions)
Chapter 14: Differentials, Errors and Approximations
Q: 9.17 | Page no. 9

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Solution for question: Using Differential, Find the Approximate Value of the ( 66 ) 1 3 ? concept: Approximations. For the courses CBSE (Commerce), CBSE (Arts), PUC Karnataka Science, CBSE (Science)
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