Unformatted text preview: the loan in 25 years. (c) Determine the total interest paid during the 25 year term mortgage. 4. Consider the hill given by the function z = f ( x, y ) = √ 4x 2y 2 4 . (a) Compute f x and f y . (b) Find the unit vector that gives the direction of steepest ascent at the point P (1 , 2). Also ﬁnd a unit vector that gives the direction of no change at that point. Sketch these two vectors and the level curve through P . (c) Suppose you’re walking over the hill along the path that is right above the path ( x ( t ) , y ( t )) = ( t, t 2 + 1) in the xyplane. As you pass the point (1 , 2 , f (1 , 2)), at what rate is your height changing? 5. Find the area of the shaded region bounded by the curves f ( x ) = x 34 x and g ( x ) =x 2 + 2 x for x ≥ 0. 1...
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 Fall '10
 MalabikaPramanik
 Math, Calculus, Constant of integration, level curve

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