X a 4 points f x x 1 3 b 4 points f x log 10 2 c 4

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x . (a) ( 4 points ) f ( x ) = x 1 / 3 (b) ( 4 points ) f ( x ) = log 10 2 (c) ( 4 points ) f ( x ) = tan(sin(4 x )) CONTINUE TO NEXT PAGE
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Math 1110 Fall 2010 Prelim 2 October 28, 2010 3 Problem 1: (cont.) (d) ( 4 points ) f ( x ) = xe - x + e 3 x (e) ( 4 points ) f ( x ) = 4 x ln x CONTINUE TO NEXT PAGE
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Math 1110 Fall 2010 Prelim 2 October 28, 2010 4 Problem 2: ( 15 points ) For each of the following functions, determine the derivative with respect to x . (a) ( 5 points ) f ( x ) = x tan( x ) ( Hint: Use logarithmic differentiation. ) (b) ( 5 points ) f ( x ) = e sin( x ) (c) ( 5 points ) f ( x ) = csc( x ) tan( x ) CONTINUE TO NEXT PAGE
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Math 1110 Fall 2010 Prelim 2 October 28, 2010 5 Problem 3: ( 15 points ) Find the slope of the tangent line to the curve y 2 + xy = sin( xy )+1 at the point (0 , 1). CONTINUE TO NEXT PAGE
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Math 1110 Fall 2010 Prelim 2 October 28, 2010 6 Problem 4: ( 15 points ) When a piece of the metal tungsten is heated to a high enough temperature, it begins to glow white hot. Tungsten is the material that glows in most incan- descent light bulbs. Nineteenth-century physicists experimentally discovered the following relationship between the power output P and the temperature T of the tungsten: P = kT 4 . This is called the Stefan-Boltzmann law. Note that in the above equation, k is a constant.
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  • Fall '06
  • MARTIN,C.
  • Continuous function

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