Handwritten Homework No 4

Handwritten Homework No 4 - special points including zero...

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Math 223 - Section 4 - Handwritten Homework Assignment # 4 Monday, September 21, 2009 Due date: Thursday, September 24, 2009 (submit immediately before or after class) This is an exam review homework, focusing on two problem areas that emerged from Exam #1. Since it only reviews material with which you should be well familiar the graded homework will contain very little feedback, and partial credit is limited in the following way: perfect answer = 10 points per problem, almost perfect answer = 5 points, not almost perfect answer = 0 points. (1) Consider the function f given by f ( x , y ) = y 4 - x 2 y 2 . Without the help of a calculator, draw a graph of the cross-section with x fixed at x = -2. Proceed as follows. Determine all values of y at which the cross-section graph is zero. Determine the slopes at these points. Determine all values of y at which the derivative of the cross-section graph is zero (extrema). Determine the values of the function at these points. Finally, draw the graph, properly labeling the axes and all
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Unformatted text preview: special points, including zero crossings and extrema, and indicate the asymptotic behavior of the function, i.e. the value of the function in the limit of large positive or negative y . (10 points) (2) Consider two vectors and v G u G with u G being a unit vector. Assume the vectors not to be parallel, and denote by θ the angle between them. Sketch the two vectors as well as the vectors and v G parr v perp G , where v parr G is the component of in the direction of , and is the perpendicular component. Using the definition of the cosine, determine the length of v v G u G v per G p parr G in terms of and the length of . Show that the length of can be expressed in terms of a simple dot product. Specify in terms of and . Finally, consider two vectors v G v G parr v parr G v G u G v G and w G with not being a unit vector. Express the length of v w G parr G ( the component of v G in the direction of w G ) in terms of an appropriate simple dot product. (10 points)...
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This note was uploaded on 09/23/2010 for the course MATH 216 taught by Professor Dickson during the Spring '10 term at UAA.

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