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In the gure abovei R is the shaded region in the rst quadrant bounded by the graph of y = 4ln(3 x); the
horizontal line y .= 6, and the vertical line x = 2
(a) Find the area of R.
(b) Find the volume of the solid generated when R is revolved about
at f be the function given by f (x) = 2x
l + x2 . I
(a) Write the rst four nonzero terms and the general term of the Taylor series for f about x = O.
(b) Does the series found in part (a), when evaluated at x = 1, converge to f (l) ? Explain why or why
Consider the differential equation 3; = 6x2 x2y. Let y = f be a particular solution to this differential
equation with the initial condition f(1) = 2. . of
I (a) Use Eulers method with two steps of equal size, starting at x = 1, to approximate f Show the
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