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Unformatted text preview: = Z 1 π (1x 4 ) dx = π ( x1 5 x 5 ) i 1 = π (11 5 ) = 4 5 π 5 5. Find the number b so that the average value of the function y = x 2 + bx + 2 on [0 , 1] is 1 3 . Average = 1 1Z 1 ( x 2 + bx + 2) dx = ( 1 3 x 3 + 1 2 bx 2 + 2 x ) i 1 = 1 3 + 1 2 b + 2 = 1 2 b + 7 3 . Set 1 2 b + 7 3 = 1 3 . Then b =4 6 6. (a) Sketch the curve with the polar equation r = θ . (b) Find the slope of the tangent line to the curve r = 2 sin θ at θ = π/ 6 dy dx = dy dθ dx dθ = d dθ (2 sin θ sin θ ) d dθ (2 sin θ cos θ ) = cos θ sin θ + sin θ cos θ cos θ cos θsin θ sin θ = sin(2 θ ) cos(2 θ ) Thus dy dx ± ± ± θ = π/ 6 = sin( π/ 3) cos( π/ 3) = √ 3 7...
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 Fall '08
 Justin
 Math, Calculus, Derivative, dx, sin sin sin

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