This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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...
View
Full
Document
This note was uploaded on 04/29/2008 for the course MATH 20B taught by Professor Justin during the Fall '08 term at UCSD.
 Fall '08
 Justin
 Math

Click to edit the document details