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221-wainger-07sp01 - Math 221 Midterm Exam(please print...

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Unformatted text preview: Math 221 Midterm Exam (please print) Name: (please print) TA’S Name! Thursday, March 1, 2007 Each Problem Worth 20 points. No calculators allowed. PROBLEM TOTAL ' VALUE 20 20 . 20 20 20 100 SCORE é) Math 221 Page 1 (1) From first principles find the equation for the tangent line to y = x2 + 211: at (2,8). Math 221 (2) Find Mm) if (ii) y(:c) = sin V :02 + 1 (111) y2 = sin($ - Page 2 Math 221 ' Page 3 (3) Suppose a particle is moving in the (51:, y)7 plane, and at time t the position of the particle is (t2 + 1, t3 + t2 + 1). Find the tangent line to the curve traced out by the particle at the point (2, 3). Math 221 I ‘ . Page 4 (4) Find the maximum and minimum of the followng functions on the given in- terval. '2 <1) 1 —~ % —2 s a: _<_ 4 .. 2 1 (11)$-- ———<a:£100. x/E ' 100 - Math 221 I Page '5 (5) A rectangle is inscribed in a circle of radius 1, with one side along the diameter of the semicircle as shown in the diagram; How should the dimensions be chosen to maximize the area of the rectan— gle? (Include the possibility that the rectangle is degenerate.) ...
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221-wainger-07sp01 - Math 221 Midterm Exam(please print...

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