course Mth 271 ÃÖªGá˜ÔdšİN¡ŒŸæN¤Œ¤DÌışƒassignment #020
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19:18:05 2.7.16 dy/dx at (2,1) if x^2-y^3=3
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RESPONSE --> 2x(dy/dx) - 3y^2(dy/dx)=0 -3y^2 = -2x -2x/-3y^2 Filling in for the x & y for the point (2,1) you get: 2(2)/3(1)^2 = 4/3 confidence assessment: 2
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19:18:45 The derivative of x^2 with respect to x is 2 x. The derivative of y^3 with respect to x is 3 y^2 dy/dx. You can see this by realizing that since y is implicitly a function of x, y^3 is a composite function: inner function is y(x), outer function f(z) = z^3. So the derivative is y'(x) * 3 * f(y(x)) = dy/dx * 3 * y^3. So the derivative of the equation is 2 x - 3 y^3 dy/dx = 0, giving 3 y^2 dy/dx = 2 x so dy/dx = 2 x / ( 3 y^2). At (2,1), we have x = 2 and y = 1 so dy/dx = 2 * 2 / (3 * 1^2) = 4/3. **
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RESPONSE --> I got the same answer for this one. self critique assessment: 2
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19:21:16 2.7.30 slope of x^2-y^3=0 at (1,1) What is the desired slope and how did you get it?
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RESPONSE --> My text had the point at (-1,1) so I solved it that way. I got the following: 2x-3y^2(dy/dx)=0 -3y^2(dy/dx) = -2x -2x/-3y^2 = 2x/3y^2 Solving for the slope you get: 2(-1)/3(1)^2 = -2/3 confidence assessment: 2
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19:21:32 The derivative of the equation is 2 x - 3 y^2 dy/dx = 0. Solving for dy/dx we get dy/dx = 2x / (3 y^2). At (-1,1) we have x = 1 and y = 1 so at this point dy/dx = 2 * -1 / (3 * 1^2) = -2/3. **
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RESPONSE --> This is the same answer that I got. self critique assessment: 2
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19:23:46 2.7.36 p=`sqrt( (500-x)/(2x))
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RESPONSE --> 2xp^2 = 500-x 2x(2p) + 2(dx/dp)(p^2)= -dx/dp (2p^2 + 1)(dx/dp) = -4xp dx/dp= -4xp/2p^2+1 confidence assessment: 2
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19:24:55 You could apply implicit differentiation to the present form, and that would work but it would be fairly messy. You have lots of choices for valid ways to rewrite the equation but I would recommend squaring both sides and getting rid of denominators. You get p^2 = (500-x) / (2x) so 2x p^2 = 500-x and 2x p^2 + x - 500 = 0. You want dx/dp so take the derivative with respect to p: 2x * 2p + 2 dx/dp * p^2 - dx / dp = 0 (2 p^2 - 1) dx/dp = - 4 x p dx / dp = -4 x p / (2p^2 - 1) **
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RESPONSE --> Some how I got my signs mixed up and I got +1 instead of -1. Sorry. self critique assessment: 2
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