Prelim1_09_29

Prelim1_09_29 - Math 1910 Prelim I 7:30-9pm Answer the...

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Math 1910 Prelim I, 7:30-9pm, September 29, 2011 Answer 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 2 cos( ) . [sin( ) 99] x dx x (10pts) (b) Find the function ( ), fx defined for 2, x < such that: (i) at any point (, ) xy on the curve ( ), y fx = the slope of the tangent to the curve is given by 2 1 , ( 2) x and (ii) the point (1,7) lies on the curve. (15pts) 2. Determine the constant 1 a > such that the area under the curve 1 y x = between 1 and x xa = is equal to 2. (15pts) 3. Consider the function 3 42 ( ) 2 , for 1 3: x f x t t dt x + ≤≤ (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.

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