Line Integral Example 2 (part 1)
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I love the colorrrssss :D made me happy :P
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Aw, I'm sad that more people haven't watched these... Ya think Sal will ever do some quantum physics stuff?
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At 0.25 you say "if I graph this when y = 0" but then you draw the line y = x.
But surely when y = 0, we get f(x,0) = x which implies that z = f(x,y) = x (I don't see how f(x) = y)
I don't see where the line y = x comes from, please can you explain?
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Hell, this is the thrill of a lifetime!!
prubeyou1 1 year ago 4
The function is f(x,y) = z = x + y-squared
In the x-z plane, y = 0, so the equation, in that plane, reduces to z = x. The first line drawn is not "y = x". It is "z = x", in the x-z plane. Then Sal draws parabolas in the y-z plane for different fixed values of x. For x = a given constant C, the equation in the y-z plane at x = C reduces to z = y-squared plus C. I think. I'm also having difficulty visualizing this function.
thyorison 1 year ago 3