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Kouba Challenge Discussion Sheet 7 1.) One hundred and forty (140) feet of fencing will be extended from a 20 ft. by 40 ft. corner of a building to create a rectangular pen. What dimensions a; and y will result in
the pen of maximum area ? / //.:2 / / X 2.) Find that number so that 4 times itself exceeds its square by the largest amount. 3.) A rectangle is inscribed beneath the graph of y = 12 — 3:2 and above the maxis. Find
the dimensions of the rectangle of a.) maximum area. b.) maximum perimeter. 4.) A piece of Wire 16 inches long is to be cut into two pieces. One piece is bent into a
circle and the other is bent into a square. Where should the out be made in order that the
sum of the areas is a a.) minimum ‘? b.) maximum ? 5.) Determine y’ = dy/da: for each. a.) w2+y2 =y+3w
b.) 4 + tan(m — y) = sec(y3)
3023; y— 1
c.) 3 =
x+y m+2 6.) Compute the slope and concavity of the graph of my + y3 = 8 at w = 0. Sketch the
graph near :3 = 0. 7.) Show that the hyperbolas my 2 1 and 3:2 — y2 = 1 intersect at right angles. 8.) The graph of the equation (x2 + y2 — 4x)2 = 45(ar2 + y2) is given. It is called a Limacon
of Pascal. Determine the slope of the line tangent to the graph at point A (:v = 1).
CHALLENGE: Determine the slope(s) of the line(s) tangent to the graph at (0,0). ...
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 Winter '09
 Kouba
 Calculus, Rectangle, Challenge Discussion Sheet, maximum area. b.

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