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Unformatted text preview: of this
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 xaxis 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
which
.
Point: x(2) = 22 + 1 = 5, y(2) = 2∙23 – 5 = 11.
Slope:
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
 Staff
 Calculus

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