Math20100Spring2010Final - The City College Department of...

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The City College Department of Mathematics Spring 2010 Ma Part I th 20100 Final Exam (70 points) Answer all questions. 1. (15pts) Find the deri ative and simplify (write without negative exponents and factor if possible): y = x 2 sin( v a. b. 3 x ) f ( x ) = x + 3 x 2 2 c. y = cos 3 ( x 2 + 2) 2. (15 pts) Compute each of the following integrals and simplify (write without negative exponents and compute any trig evaluations): x a. + 3 x 2 2 dx b. ( ) 2 3 3 6 8 4 x dx x x + + Page 1 of 3 c. 3 4 sin(5 ) x dx π π 3. (6pts) Find (2) f as a reduced fraction, where 2 3 5 ( ) x f x x x + = . (You do not have to e expression for simplify th f ( ) x ). = 2 + 2 4. (6p ) ts For x y 2 3 + a. Find dy . x 2 y dx b. Find the slope of the curve at ( 1, 1) . 5. (6pts) Find n the area u der the graph of y = sin x over the interval [ ] 4, π π . , 6. (7p ) ts For f ( x ) = 1 x 2 a. Use the limit definition to find ( ) f x . b. Find the equation of the tangent line to f ( x ) at x = − 2 .
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