Answer:
Let x = 25 Now, \[x+\Delta \,x=25.1\] \[\Rightarrow \]\[\Delta \,x=25.1-25\]\[\Rightarrow \]\[\Delta \,x=0.1\] Again, let \[y=\frac{1}{\sqrt{x}}\]\[\Rightarrow \]\[\frac{dy}{dx}=\frac{-\,1}{2{{x}^{3/2}}}\] \[\Rightarrow \] \[{{\left( \frac{dy}{dx} \right)}_{x\,\,=\,\,25}}=\frac{-\,1}{2\,{{(25)}^{\frac{3}{2}}}}=-\frac{1}{250}=-\,0.004\] Also, \[\Delta y={{\left( \frac{dy}{dx} \right)}_{x\,\,=\,\,25}}(\Delta x)=(-\,0.004)\,\,(0.1)\] \[=-\,0.0004\] \[\Rightarrow \] \[\frac{1}{\sqrt{25.1}}=y+\Delta y\] \[=\frac{1}{\sqrt{x}}+(-\,0.0004)=\frac{1}{\sqrt{25}}-0.0004\] \[=\frac{1}{5}-0.0004=0.2-0.0004\] \[\therefore \] \[\frac{1}{\sqrt{25.1}}=0.1996\]
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