1007Test4sol_09

1007Test4sol_09 - Test 4 Wednesday MATH 1007 G Last Name ID...

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Test 4, Wednesday,March 18, 2009 MATH 1007 G Page 1 of 3 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 Ans. (a) lim x x e x x - - 0 4 2 1 4 = lim x x e x - 0 4 4 4 2 ( L’Hopital’s rule due to 0/0 form) = - 2 1 0 4 lim ( ) x x e x = 2 4 1 0 4 lim x x e ( L’Hopital’s rule due to 0/0 form) = 8 0 4 lim x x e = 8 (b) lim x x x e →∞ - 3 2 = lim x x x e →∞ 3 2 = →∞ lim x x x xe 3 2 2 2 ( L’Hopital’s rule due to ∞ ∞ / form) = →∞ lim x x x e 3 2 2 = →∞ lim x x xe 3 4 2 ( L’Hopital’s rule due to ∞ ∞ / form) =0 Question 2. [4 marks] Find the absolute maximum and absolute minimum value of f x x x ( ) = + 2 1 on the interval [0,3]. Solution: f x x x x x x x ' ( ) ( )( ) ( )( ) ( ) ( ) = + - + + = - + 2 2 2 2 2 2 1 1 2 0 1 1 1 So, f x x ' ( ) = ⇔ = ± 0 1 f x ' ( ) DNE ⇔ = - x 2 1 which has no solutions. Critical points on the interval
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1007Test4sol_09 - Test 4 Wednesday MATH 1007 G Last Name ID...

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