its can be shown that while deltax = dx, deltay is not neccesarily equal to dy. show this is true by comparing deltay and dy using the following.

y=1-2x^2, x=2 and deltax=0.01
differentials i get the right answer for deltay=0.0401 but i get dy=-0.08 so i am lost

Question

its can be shown that while deltax = dx, deltay is not neccesarily equal to dy. show this is true by comparing deltay and dy using the following.

y=1-2x^2, x=2 and deltax=0.01 
differentials i get the right answer for deltay=0.0401 but i get dy=-0.08 so i am lost

anonymous · Answer

$$y=1-2x^2$$First:$$y(2)=1-2*(2)^2=-7\y(2+\Delta x)=y(2+0.01)=y(2.01)=1-2*(2.01)^2=-7.0802$$$$\Delta Y=y(2.01)-y(2)=-7.0802-(-7)=0.0802$$Now we have to do the derivative of y(x)$$y'(x)=-4x$$$$y'(2)=-8\y'(2.01)=-8.04$$$$dy=y'(2.01)-y'(2)=-8.04-(-8)=0.04$$

anonymous · Answer

umm, shouldnt the answers be negative?

anonymous · Answer

ohh, sorry, my mistake.$$dy=y'(2.01)-y'(2)=-8.04-(-8)=-0.04$$

anonymous · Answer

same thing with

anonymous · Answer

$$DeltaY$$

anonymous · Answer

$$\Delta Y=-0.0802$$

anonymous · Answer

thaank you that cleared up that thank you