math20100fall2011 - The City College Department of...

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The City College Department of Mathematics Fall 2011 Math 20100 Final Exam CALCULATORS are NOT allowed, NO scrap paper (use sheets provided) Part I (questions 1 to 8): Answer all questions (70 points) 1) Find dy dx for each of the following. Simplify (a) and (c) as indicated (4 points each). (a) 32 9 yx x =− Write the answer as a single simplified fraction (b) cos (4 ) x = (c) 2 23 2 (1 ) x y x = + Write the answer as a single simplified fraction 2) Find each integral (4 points each). 3) (4 points) For the function defined implicitly by the equation 5 3 y + = find the derivative at the point . y (2,1) 4) (4 points) Find the area of the region under the curve 2sin = and above the x- axis lying between the lines 4 x = and 2 x = . Include a sketch of the region. 5) (8 points) A person 6 feet tall walks away from a street light which is 24 feet above the ground. (a) How long is the person's shadow, when the person is standing 9 feet from the street light? Justify your answer.
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