winter2000 sample midterm1

winter2000 sample midterm1 - mug is 12 cm how fast will the...

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Math 20 Winter 2000 Prof. Moore Sample Midterm 1 Directions: You may use a graphing calculator to graph and compute things during the exam, but you may not use any notes or books, or receive help from any other person. Show all of your work, explaining as much as possible. 1. If a rectangle has its base on the x -axis and two vertices on the curve y = e - x 2 , show that the rectangle has the largest possible area when the two vertices are at the points of inflection of the curve. 2. CoFee is being poured at a constant rate of 2 cm 3 /sec into a mug whose inside is shaped like a truncated cone. If the upper and lower radii of the mug are 4 cm and 2 cm and the height of the
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Unformatted text preview: mug is 12 cm, how fast will the coFee level be rising when the coFee is halfway up? 3. ±ind the following limits: a) lim x → π/ 2 sin(2 x ) 4 x 2-π 2 b) lim x → 1 x 3-x 2 + x-1 x 3-x 2 c) lim x →∞ 3 x 4-5 x 2 + x-3 1 + x 2 + x 4 d) lim x →∞ µ x + 3 x-3 ¶ x e) lim x →∞ e x x n 4. ±ind the highest and lowest points on the curve x 2 + xy + y 2 = 12. 5. A cone is made from a circular piece of paper of radius R by cutting out a wedge-shaped sector and joining the remaining edges. ±ind the maximum capacity of such a cone....
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