Midterm1 - T F If f ( 3 ) = g ( 3 ) then the tangent lines...

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Test 1 Math 102 June 6, 2011 NAME: STUDENT #: Time: 60 minutes Policy on Academic Integrity Academic integrity requires commitment to the values of honesty, trust, fairness, respect, and responsibility. It is expected that students, faculty members and staff at the University of Victoria, as members of an intellectual community, will adhere to these ethical values in all activities related to learning, teaching, research and service. 1
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Problem 1: ( 5 points ) Consider the function f ( x ) = 1 + 1 1 + 1 x . Compute the following limits: lim x 0 f ( x ) , lim x →- 1 - f ( x ) , lim x f ( x ) . Problem 2: ( 5 points ) True or False? T F No rational function can have two horizontal asymptotes. T F No function can have more than two horizontal asymptotes. T F There exist differentiable functions which are not continuous.
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Unformatted text preview: T F If f ( 3 ) = g ( 3 ) then the tangent lines to the graphs of f and g at x = 3 coincide. T F There exists a function which is continuous on [ , 1 ] and has a vertical asymptote at x = 1 2 . 2 Problem 3: ( 5 points ) Find y 00 if x 3 + y 3 = 1. 3 Problem 4: ( 5 points ) Let f ( x ) = x 2 + 1. Using the limit denition, nd f ( 1 ) . Then nd the equation of the tangent line to the graph of f where x = 1. 4 Problem 5: ( 5 points ) Consider the function g ( t ) = ( 1- t ) 2 1-t a) Compute the derivative of g ( t ) . b) Find the vertical and the horizontal asymptotes of g ( t ) . Justify! 5...
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Midterm1 - T F If f ( 3 ) = g ( 3 ) then the tangent lines...

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