Use of differentials to approximate

**av8or91** · February 9th, 2010, 06:23 PM

use differential to approximate Square root 17.

**VonNemo19** · February 9th, 2010, 06:31 PM

Originally Posted by av8or91

use differential to approximate Square root 17.

Have you tried anything here?

**av8or91** · February 9th, 2010, 08:13 PM

I know we need to do something with the closes square root which is 16. I just can remember how to do the rest.

**dedust** · February 9th, 2010, 08:38 PM

Originally Posted by av8or91

I know we need to do something with the closes square root which is 16. I just can remember how to do the rest.

use $f(x + \triangle x) \approx f(x) + f'(x) \triangle x$ with $f(x) = \sqrt{x}$

**av8or91** · February 10th, 2010, 10:17 AM

Im still not 100 percent getting this. Could someone show me how to do it? Thanks

**Keithfert488** · February 10th, 2010, 12:00 PM

$\sqrt{17}=f(x+\Delta x)$
Where $x=16$ , $\Delta x=1$ , and $f(x)=\sqrt{x}$

$f(x+\Delta x)\approx f(x)+{f}'(x)\Delta x$

${f}'(x)=\frac{\mathrm{d}[\sqrt{x}]}{\mathrm{d} x}=\frac{1}{2\sqrt{x}}$

$f(17)\approx f(16)+(1){f}'(16)=4+\frac{1}{8}=33/8=4.125$

I hope this helps.

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