Unformatted text preview: (b) Find the straight line passing through the point P and intersect the line L at the right angle. Hint: ﬁnd the direction vector for this line ﬁrst via Fig 11.43. 6. Do the following limit exist? If yes, ﬁnd them (a) lim ( x,y ) → (0 , 0) x 2 +2 xy + y 2 x + y . (b) lim ( x,y ) → (0 , 0) x 2 +2 xy + y 2 x 2 + y 2 . 7. Find the following for the vector function F ( t ) = ( t 2 ,e 2 t +3 , sin t ). (a) lim t → F ( t ) . (b) d dt F ( t ) . (c) R F ( t ) dt. 8. Find the tangent line of the curve x = ( t 2 ,e 2 t +3 ,sint ) at t = 0. 9. Graph the surface z 2x 2y 2 = 0. 10. Assume a particle is moving with a constant speed. Show that its velocity v ( t ) must be perpendicular to its acceleration. Here t is the time. Hint the assumption means  v  2 = v · v = constant. 11. Find the partial derivatives f x ,f y ,f xx ,f xy for f ( x,y ) = x 2 y 3 + sin( x/y ). 1...
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 Fall '09
 Phann
 Multivariable Calculus, Vectors, Vector Space, Euclidean geometry

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