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revf-s-08

# revf-s-08 - Review for Final Exam 1 Know the rst ve...

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Review for Final Exam 1. Know the first five Maclaurin series in Table 1, p 743. 2. 11.10: 29-30, 33, 34, 63-68 3. 10.3: 29, 31, 33, 34, 41, 42, 54 and 69 To do 54, we convert the given cartesian equation to a polar equation and notice that the graph of the polar equation is simply the four leaf rose curve given in Problem 4 (b) in this review. 4. (a) Find a cartesian equation for the polar graph of each equation: r = 6 sin θ, r = 4 cos θ + 5 sin θ, r = 1 2 cos θ + 3 sin θ (b) Draw the polar graph of r = sin 2 θ. (c) Draw the graph of r 2 = sin 2 θ . To do Part (c) in problem 4, we should start with the graph in Part (b). If ( r, θ ) satisfies the equation in Part (b), we see that r < 0 if θ is in the 2nd or 4th quadrant. This is because sin 2 θ < 0 if θ is in these quadrants. Thus r 2 6 = sin 2 θ if θ is in these two quadrants. This means that no point from the 2nd nor 4th quadrant can be on the graph in Part (c). So to draw the graph in Part (c), we simply take the graph in Part (b), eliminate the leaves in the 2nd & 4th quadrants, and fatten the leaves in the first & third quadrants.

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revf-s-08 - Review for Final Exam 1 Know the rst ve...

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