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problem, but what the heck?
And the vertical line through the focus goes from to . . So, here is the sketch, with a little strip added for the approximating phase. x Note that we don't need to revolve the entire region around the x-axis to get the solid of revolution; we can
revolve just the upper half. The volume contributed by that little (blue) strip is
So the total volume would be given by the integral
6. Find the equation of the line tangent to the parameterized curve
Point: x(2) = 22 + 1 = 5, y(2) = 2∙23 – 5 = 11.
Equation: y – 11 = 3(x – 5). , so m = 3. , at the point for 7. Find the Cartesian form of the equation for the parameterized curve ; 0 ≤ t ≤ 2π. , I'm going to add a multiple of x2 = 4 sin2t to a multiple of y2 = 9 cos2t. Here it is.
In a more standard form: . 8. Find the length of the curve given by , , from to . After the (optional, this time) sketch, everything starts with
that applies to this context, . Rewriting that in the form . And so the length of the ar...
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This document was uploaded on 03/18/2014 for the course MATH 237 at Frostburg.
- Fall '1