119Mdt2 - 2 dx (b) 2 π Z p | sin θ | 119 + | sin θ | +...

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Last Name Name Student No.: Department: Section: Signature: : : : : : : : : : : Code Acad.Year Semester Date Time Duration M E T U Northern Cyprus Campus Calculus and Analytical Geometry II. Midterm Math 119 2007-2008 Fall 9.12.2007 10:00 120 minutes 6 QUESTIONS ON 6 PAGES TOTAL 100 POINTS 1 2 3 4 5 6 1. (5+5+5+5=20 points) Let f ( x ) = x 2 + 4 x 2 - 4 (a) Find the domain of f and its asymptotes, if any. (b) Find the critical points of f , if any. (c) Determine the intervals where f is concave up/down. (d) Sketch the graph of f .
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2. (10 points) Find the area of the largest rectangle that can be inscribed in a right triangle with perpendicular sides of length 3 cm and 4 cm , if the two sides of the rectangle lie along these sides of the triangle.
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3. (5+5+5=15 points) Evaluate each of the following integrals. (a) Z x 3 (2 x 4 + 7)
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Unformatted text preview: 2 dx (b) 2 π Z p | sin θ | 119 + | sin θ | + 1cos θdθ (c) 2 Z 1 ( x + 1 x ) 2 dx 4. (a) (10 points) If f ( x ) is differentiable, and x Z f ( t ) dt = f ( x ) 2 for all x , find f ( x ). (b) (10 points) Find F ( x ) if F ( x ) = 2 x Z x tdt t 3 + 1 dt 5. (5+10=15 points) (a) Sketch the region enclosed by y = | x | and y = x 2-1. (b) Find the area of the region. 6. (a) (10 points) Find the volume of the solid obtained by rotating the area bounded by y = sec x , y = 0, x = 0 and x = π/ 3 around the x-axis. (b) (10 points) Find the volume of the solid obtained by rotating the area bounded by y = 1 (1 + x 2 ) 2 , y = 0, x = 1 and x = 2 around the y-axis....
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119Mdt2 - 2 dx (b) 2 π Z p | sin θ | 119 + | sin θ | +...

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