1007Test4_09

1007Test4_09 - Test 4, Wednesday,March 18, 2009 MATH 1007 G...

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Test 4, Wednesday,March 18, 2009 MATH 1007 G Page 1 of 4 Last Name :_________________ First Name:_______________ ID #:____________________ No Calculators are allowed. Show your work Question 1. [5 marks] Use L’Hospital’s rule to evaluate the following limits. For each application, explain why the rule applies. (a) lim x x e x x - - 0 4 2 1 4 (b) lim x x x e →∞ - 3 2 Question 2. [4 marks] Find the absolute maximum and absolute minimum value of f x x x ( ) = + 2 1 on the interval [0,3].
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Test 4, Wednesday,March 18, 2009 MATH 1007 G Page 2 of 4 Question 3. [4 marks] Let f be a continuous function with the following properties. a) Domain is ( , ) - ∞ ∞ b) x,y intercepts are (0,0). c) f is an odd function. d) lim ( ) x f x →∞ = - 2 e) f x ' ( ) < 0 for 0<x<2, f x ' ( ) 0 for x>2. f) f x '' ( ) 0 for 0<x<3, f x ''( ) < 0 for x>3. Use this information to sketch the graph when x>0 and then use the fact that f is odd to sketch the graph when x<0. Question 4. [3 marks]
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1007Test4_09 - Test 4, Wednesday,March 18, 2009 MATH 1007 G...

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