approximation. calc 3

mcwang719

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Mar 22, 2006
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Approximate f(0.1,0.95,44degrees) where f (x,y,z)= ( e^-xy) sin z. You may evalutate f only once, and that evalutation must be at the point (0,1, 45 degree). Remember you must work in radians.

I kinda confused on what the problem is asking. Doesn't approximating mean taking the partial derivative and plugging in (0.1,0.95,44degree). But when it states "you may evalutate f only once, and that evalutation must be at the point (0,1,45degree)" it seems like there's is more to the problem. i was reading my textbook and found an example on linear approximation. is that what i need to do? thanks!!!!!
 
You are close.
Take the derivitive then "plug in" dx=.1, dy=-.05 and dz=-1*pi/180. I'm not sure what "evaluate only once" means 'cause you have to evaluate f' at (0,1,45) when you do the plug ins.
Think about
f(x) = y = x^2 for x=3.1
f(x)=f(3)=9
dx=.1
dy = 2x*(dx)
d(f(3)) = 2*3*(.1) = .6
(3+.1)^2 ~= f(3)+d(f(3)) = 9+.6
That's the general idea.
 
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