5.[23.8, 3.8] by [22.5, 2.5]The graph passes through the pole when r53 cos u50,which occurs when u5}p2}and when u5}32p}. Since the u-interval 0 #p#1 produces the entire graph, we needonly consider u5}p2}. At this point, there appears to be avertical tangent line with equation u5}p2}(or x50).Confirm analytically:x5(3 cos u) cos u53 cos2uy5(3 cos u) sin u}dduy}5(23 sin u)sin u1(3 cos u)cos u53(cos2u2sin2u)and }ddux}56 cos u(2sin u). At 10,}p2}2,}ddux})u5p/250, and }dduy})u5p/253(02212)5 23. So at 10,}p2}2,}ddux}50 and }dduy}0, so }ddyx}is undefined and the tangent line is vertical.6.[23, 3] by [22, 2]A trace of the graph suggests three tangent lines, one withpositive slope for u5}p6}, a vertical one for u5}p2}, and onewith negative slope for u5}56p}. Confirm analytically:}dduy}5 26 sin 3usin u12 cos 3ucos uand}ddux}5 26 sin 3ucos u22 cos 3usin u.
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