Section 11 6 5 10 12 9 47 PM Ali Al Zaabi MA 242 section 001 Spring 2012 Instructor J Louis Capps WebAssign Section 11 6 Homework Current Score 24 25 24 25 Due Monday February 27 2012 11 05 PM EST The due date for this assignment is past Your work can be viewed below but no changes can be made 1 2 2 points Previous Answers Find the directional derivative of f at the given point in the direction indicated by the angle f x y sin x 2y 4 2 3 4 0 707 0 707 2 2 2 points Previous Answers Find the directional derivative of the function at the given point in the direction of the vector v f x y z x y z 4 1 1 v 1 2 3 1 2 1 2 3 1 1 points Previous Answers Use the figure to estimate Du f 2 2 3 3 4 2 2 points Previous Answers Find the directional derivative of f x y z x2 y2 z2 at P 2 1 3 in the direction of the origin 7 48 7 48 5 3 3 points Previous Answers Find the maximum rate of change of f at the given point and the direction in which it occurs http www webassign net web Student Assignment Responses view key dep 3769836 Page 1 of 3 Section 11 6 5 10 12 9 47 PM f x y ln x2 y2 1 2 Maximum rate of change 0 894 0 894 Direction Enter as a vector of magnitude 1 0 447 0 447 0 894 0 894 6 4 4 points Previous Answers Find the maximum rate of change and the gradient of f at the given point f x y z x2y3z4 1 1 1 Maximum rate of change 5 39 5 39 Gradient 2 2 3 3 4 4 7 2 25 2 25 points Previous Answers Near a buoy the depth of a lake at the point with coordinates x y is z 200 0 02x2 0 001y3 where x y and z are measured in meters A fisherman in a small boat starts at the point 80 60 and moves toward the buoy which is located at 0 0 a Find Du f 80 60 3 92 3 92 b Is the water under the boat getting deeper or shallower when he departs deeper shallower 8 5 5 points Previous Answers The temperature at a point x y z is given by the following where T is measured in C and x y z in meters 2 2 2 T x y z 200e x 3y 9z a Find the rate of change of temperature at the point P 2 1 2 in the direction toward the point 3 3 3 Do this on paper Your teacher may ask you to turn in this work http www webassign net web Student Assignment Responses view key dep 3769836 Page 2 of 3 Section 11 6 5 10 12 9 47 PM b In which direction does the temperature increase fastest at P Enter as a vector of magnitude 1 0 109 0 109 0 163 0 163 0 981 0 981 c Find the maximum rate of increase at P C m 9 3 3 points Previous Answers Suppose that you are climbing a hill whose shape is given by the equation z 1000 0 01x2 0 02y2 and you are standing at a point with coordinates 60 100 764 a In which direction should you proceed initially in order to reach the top of the hill fastest Enter as a vector of magnitude 1 0 287 0 287 0 958 0 958 b If you climb in that direction at what angle above the horizontal in degrees will you be climbing initially 76 5 76 5 http www webassign net web Student Assignment Responses view key dep 3769836 Page 3 of 3
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