Find the approximate value of √0.037
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Posted by Rashmi Mishra 8 years, 3 months ago
- 2 answers
Gurvinder Kaur 7 years, 10 months ago
Take {tex}y = \sqrt x {/tex}
Let x=0.04 and {tex}\Delta x{/tex}=-0.003, Then
{tex}\Delta y = \sqrt {x + \Delta x} - \sqrt x {/tex}
{tex}\Delta y = \sqrt {0.037} - \sqrt {0.04} {/tex}
{tex}\sqrt {0.037} = \sqrt {0.04} + \Delta y{/tex}
{tex}\sqrt {0.037} = 0.2 + \Delta y{/tex}
Now, dy is approximately equal to {tex}\Delta y{/tex} and is given by
{tex}dy = \left( {\frac{{dy}}{{dx}}} \right)\Delta x{/tex}
{tex} = \frac{1}{{2\sqrt x }}\left( { - 0.003} \right){/tex}
{tex} = \frac{1}{{2\sqrt {0.04} }}\left( { - 0.003} \right){/tex}
{tex} = - 0.0075{/tex}
Thus, the approximate value of {tex}\sqrt {0.037} {/tex} is 0.2 - 0.0075 = 0.1925
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Harman Deep 5 years, 2 months ago
0Thank You