Change in y and differentrial dy

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October 10th 2009, 01:54 PM
mybrohshi5

Change in y and differentrial dy

Let http://webwork.asu.edu/webwork2_file...29773ea691.png.
Find the change in http://webwork.asu.edu/webwork2_file...22b824af51.png, http://webwork.asu.edu/webwork2_file...c0174d9fa1.png when http://webwork.asu.edu/webwork2_file...556151e691.png and http://webwork.asu.edu/webwork2_file...2de99d6b61.png
Find the differential http://webwork.asu.edu/webwork2_file...e5fc553981.png when http://webwork.asu.edu/webwork2_file...556151e691.png and http://webwork.asu.edu/webwork2_file...735004e061.png

can i get some help with this please?

thank you
October 10th 2009, 02:02 PM
Mush

Quote:

Originally Posted by mybrohshi5

Let http://webwork.asu.edu/webwork2_file...29773ea691.png.
Find the change in http://webwork.asu.edu/webwork2_file...22b824af51.png, http://webwork.asu.edu/webwork2_file...c0174d9fa1.png when http://webwork.asu.edu/webwork2_file...556151e691.png and http://webwork.asu.edu/webwork2_file...2de99d6b61.png
Find the differential http://webwork.asu.edu/webwork2_file...e5fc553981.png when http://webwork.asu.edu/webwork2_file...556151e691.png and http://webwork.asu.edu/webwork2_file...735004e061.png

can i get some help with this please?

thank you

Currently, $y = f(x)$

So we can say that $y + \Delta y = f(x+ \Delta x)$

We can then re-write this as: $\Delta y = f(x+\Delta x) - y$

And we know that $y = f(x)$ , so we can say:

$\Delta y = f(x+\Delta x) - f(x)$

We know that $f(x) = 4 \sqrt{x}$

So:

$\Delta y = 4 \sqrt{x + \Delta x} - 4 \sqrt{x}$

For the second part, just differentiate it and then take it from there.
October 10th 2009, 02:03 PM
Arturo_026

for the first one use the formula;
http://webwork.asu.edu/webwork2_file...c0174d9fa1.png= f(x+delta(x))-f(x)
and for the other
dy=f'(x)dx