100hw3 - y = x 3 . 5. (13.3, 44) Let w = p x 2 + 5 y 2-z 2...

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Math 100 Homework 3 fall 2010 due 15/10 1. (12.3, 8) Find the arc length of the curve r ( t ) = ( 1 2 t, 1 3 (1 - t ) 3 / 2 , 1 3 (1 + t ) 3 / 2 ) - 1 t 1 . 2. (12.3, 30) Find an arc length parametrization of the curve r ( t ) = (sin e t , cos e t , 3 e t ) t 0 . 3. (13.1, 56) Describe the level surfaces in words of f ( x, y, z ) = z - x 2 - y 2 . 4. (13.2, 34) (a) Show that the value of x 3 y 2 x 6 + y 2 approaches 0 as ( x, y ) (0 , 0) along any straight line y = mx , or along any parabola y = kx 2 . (b) Show that lim ( x,y ) (0 , 0) x 3 y 2 x 6 + y 2 does not exist by letting ( x, y ) (0 , 0) along the curve
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Unformatted text preview: y = x 3 . 5. (13.3, 44) Let w = p x 2 + 5 y 2-z 2 , ±nd ∂w/∂x | (2 , 1 ,-1) , ∂w/∂y | (2 , 1 ,-1) and ∂w/∂z | (2 , 1 ,-1) . 6. (13.3, 66) Find ∂w/∂x , ∂w/∂y and ∂w/∂z if ln(2 x 2 + y-z 3 + 3 w ) = 4 z. 7. (13.5, 54) Let f be a di²erentiable function of three variables and suppose that w = f ( x-y, y-z, z-x ). Show that ∂w/∂x + ∂w/∂y + ∂w/∂z = 0 . 1...
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