This preview shows page 1. Sign up to view the full content.
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 nd 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 youre 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...
View
Full
Document
This note was uploaded on 01/14/2012 for the course MATH 105 taught by Professor Malabikapramanik during the Fall '10 term at The University of British Columbia.
 Fall '10
 MalabikaPramanik
 Math, Calculus

Click to edit the document details