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Math Help - calculus

  1. #1
    Junior Member
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    Dec 2008
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    calculus

    These are slope direction fields, can anyone tell me what they mean?
    I need to match them to equations such as y'= 1/x , y'= 1/y , y'= e^(-x^2), y'= y^2 -1, y'= (x+y)/(x-y), and y'= (sinx)(siny)
    If you click on the pic it gets bigger and easier to read
    Attached Thumbnails Attached Thumbnails calculus-photo-19.jpg  
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  2. #2
    MHF Contributor
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    Slope fields seem hard but they are not. This is common in math I think - easy things seeming hard and hard things seeming easy. Anyway, the basic idea is that a slope field of a derivative indicates visually the slope at each point. So if you look at the point (1,1) or close to it if it's unmarked then the direction and slope of the line segment indicate the slope at that point. The best way to do a multiple choice problem like this is to pick one derivative and try to match it to its graph. Look at a graph and pick some points in different quadrants or simply not close together and take note of what the slope should be. Then you should be able to find the slope field which is true for all the points you picked and you have found a match. Repeat process for others. Take note however, if the slope fields are very similar looking pick points to test at areas where they are different.
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