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Test2 - Student's Name Test 2(Sections 2.7 2.8 3.1 to 3.6...

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Student’s Name: Test 2 (Sections 2.7, 2.8, 3.1 to 3.6, and 3.9) MAC2311, Section 17, Instructor: Ms. Hoa Nguyen ([email protected]) Problem 1 ( 10pts ) Determine or not whether f (0) exists. If its exists, give its value. Otherwise, write DNE. f ( x ) = x 2 sin( 1 x ) if x = 0 0 if x = 0 Problem 2 ( 5pts ) Use lim x 0 sin x x = 1 to find lim x 0 sin 2 (2 x ) x 2 . Problem 3 ( 10pts ) Find a second-degree polynomial f ( x ) = ax 2 + bx + c such that the following conditions are met: f (4) = 9, f (4) = 3 and f (4) = 3. Problem 4 ( 10pts ) If x 2 + xy = 10, find dy dx when x = 2. Problem 5 ( 10pts ) If a ball is thrown vertically upward with a velocity of 4 ft/s, then its height in feet after t seconds is given by s = 4 t - 2 t 2 . What is the maximum height reached by the ball? Problem 6 ( 10pts ) At what point on the given curve y = 9 + 6 e x - 6 x is the tangent line parallel to the line 30 x - y = 4. Problem 7 ( 10pts ) Find ALL points at which the tangent line is horizontal on the graph of the function y = 6 sin x + sin 2 x .
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