Let f(x, y) = − cos(x + y2 ) and let a be the point a...

Let f(x, y) = − cos(x + y² ) and let a be the point a = ( π/2, 0).

(a) Find the direction in which f increases most quickly at the point a.

(b) Find the directional derivative Duf(a) of f at a in the direction u = (−5/13 , 12/13) .

(c) Use Taylor’s formula to calculate a quadratic approximation to f at a.

Expert Solution

milcah answered 2 years ago

f(r,?) f(x,y) r(cos(?)) = x r(cos(2?)) = ? r(cos(3?)) = x3-3xy2/x2+y2 r(cos(4?)) = ? r(cos(5?)) =...

f(r,?) f(x,y) r(cos(?)) = x r(cos(2?)) = ? r(cos(3?)) = x3-3xy2/x2+y2 r(cos(4?)) = ? r(cos(5?)) = ? Please complete this table. I am having trouble converting functions from polar to cartesian in the three dimensional plane. I understand that x=rcos(?) and y=rsin(?) and r2 = x2 + y2 , but I am having trouble understanding how to apply these functions.

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