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SecJEx2W01

# SecJEx2W01 - r s and z = sin r s 7(a Find the directional...

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Murat Atmaca Winter 2001 Math 22 Exam#2 1. Given the function z = ln(4 x + 2 y - 8) 2 x - y - 4 , find and Sketch the domain of the function. 2. Evaluate e 0 . 1 + sin( - 0 . 2). 3. Find the limit, if it exists, or show that the limit does not exist for lim ( x,y ) (0 , 0) (2 x + 3 y ) 3 8 x 3 + 27 y 3 . 4. Find the local maximum and minimum values and the saddle points of the function f ( x, y ) = x 2 + 2 y 2 - x 2 y + 5 . 5. Find an equation of the tangent plane to the surface cos( πx ) - x 2 y + e xz + yz = 4 at the point P(0,1,2). 6. Find ∂w ∂r and ∂w ∂s when r=1 and s=-1 If w = (2 x + 3 y + 4 z ) 2 , x =
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Unformatted text preview: r + s ) and z = sin( r + s ). 7. (a) Find the directional derivative of the function f ( x, y, z ) = x 3-xy 2-z at the point P(1,1,0) in the direction from Q(1,-1,1) to R(3,-2,7). (b) In what direction does of change most rapidly at P, and what are the rates of change in these directions. 8. Show that f ( x, y ) = e-x cos( y )-e-y cos( x ) satisﬁes Laplace’s Equation ∂ 2 f ( x, y ) ∂x 2 + f yy ( x, y ) = 0....
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