Math 1910 Prelim I, 7:30-9pm, September 29, 2011Answer the following 5 questions. Show all work. Closed book, no calculators; 1-sided (8.5 x 11) “cheat sheet” is allowed – individually and uniquely hand-written (without collaboration) – will be collected along with the exams – will not be returned. Academic integrity on the part of each student is presumed. Violations will be dealt with swiftly and justly. 1. (a) Solve 2cos( ).[sin( ) 99]xdxx−∫(10pts) (b) Find the function ( ),fxdefined for 2,x<such that: (i) at any point (, )xyon the curve ( ),y fx=the slope of the tangent to the curve is given by 21,(2)x−and (ii) the point (1,7) lies on the curve. (15pts) 2. Determine the constant 1a>such that the area under the curve 1yx=between 1 and xxa=is equal to 2. (15pts) 3. Consider the function342( )2, for 13:xf xtt dtx≡+≤≤∫(a) Find ( ).′(10pts) (b) Are there any critical points, i.e., points
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This note was uploaded on 10/31/2011 for the course MATH 1910 at Cornell.