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Unformatted text preview: How do you graph the surface z = sin 2 over the annulus R from our example in the 17.3 notes? How would you graph the corresponding solid whose volume we were finding? First off, lets consider the graph of sin 2 vs. in Cartesian coordinates: The square of a real number in [0,1] will also be in [0,1]. Because the range of sin is [0,1], the range of sin 2 is also [0,1]. Unlike the graph for sin , there are no corners at -values of 0, , 2 , etc. The sin 2 function is everywhere differentiable! Its derivative is given by 2sin cos , or sin 2 ( ) , which is 0 at = n n integer ( ) . How do you graph z = sin 2 in 3-space? Heres what Mathematica gives; the coordinate axes are rotated a bit differently from what were used to. How do we get the piece over R ? You could take scissors to the previous graph, and rotate the scissors as you cut. It's basically like a twisty slide, or a piece of a roller coaster. Imagine a staircase in a mansion that is curving upward, except that we smooth out the...
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