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Unformatted text preview: t = 0, so, T (0) = h 1 , 1 , 1 i / √ 3. Furthermore, N ( t ) = T ( t ) /  T ( t )  = h cos ,tsin t,sin tcos t, i / √ 2 , and N (0) = h 1 ,1 , i / √ 2. Finally, B (0) = T (0) × N (0) = h 1 ,1 , 2 i / √ 6. 1 Problem 5. Does the limit lim ( x,y ) → (0 , 0) xy x 2 + y 2 exist? Why? Solution: The limit does not exists, because the limit =0 on the line y = x , while the limit = ∞ on the line y = 0. Problem 6. For f ( x,y,z ) = √ x + yz , ﬁnd the rate of change of at P (1 , 3 , 1) in the direction of the vector v = h 2 , 3 , 6 i . Solution: The rate of change is equal to ∇ f ( P ) · u where u is the unit vector in the direction v . Now, ∇ f (1 , 3 , 1) = h 1 , 1 , 3 i / 4 and u = h 2 , 3 , 6 i / 7. Thus, the answer is 23/28....
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This note was uploaded on 12/15/2011 for the course MAC 2313 taught by Professor Keeran during the Spring '08 term at University of Florida.
 Spring '08
 Keeran
 Calculus, Geometry

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