# 1997 - The City College of New York Department of...

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The City College of New York Department of Mathematics Math 20100 Final Exam Spring 2009 Instructions : No electronic device of any sort may be used during this exam. Please show all work in the space provided following each question. The time for the exam is 2 hours, 15 minutes. Part I: Do all 10 problems (70 points) 1. Let 2 2 2 1 x y x + = + . Using rules of differentiation find y . Express your answer as a quotient in simplified form. (5 points) 2. Let . Using rules of differentiation find 2 cos (3 ) yx x = y . Express your answer as a sum in simplified form. (5 points) 3. Let () 13 16 32 f xx x =+ . Find () fx and (4) f . (5 points) 4. Evaluate 2 2 23 1 dx x −+ . (5 points) 5. Evaluate 1 0 81 dx x + . (5 points) 6. Evaluate 4 cos sin x xdx . (5 points) 7a) Let f x = x . State the definition of the derivative as a limit and use the definition to find . (No credit will be given for finding the derivative using any other method.) (5 points) b) Using the answer to 7a), what is the equation of the tangent line to the graph of at ?

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1997 - The City College of New York Department of...

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