ep6 - 92.131 Calculus 1 l'Hpital's Rule Determine the...

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92.131 Calculus 1 l’Hôpital’s Rule Determine the following limits: 1) x e x x 1 lim 0 2) x x x sin lim 0 3) 2 0 cos 1 lim x x x 4) 1 1 lim 2 2 + x x x 5) x x e x lim 6) x x x ln lim 7) 8) x x x x xe 2 lim x ln lim 0 + 9) 1 2 ln lim 2 2 1 + + x x x x x x x 10) 1 2 1 ) sin( lim 2 1 1 + + x x x x x π 11) x x x csc ) (cos 0 lim + 12) 2 2 2 1 ) 1 ( 2 lim x x x x 13) 1 lim 2 0 x e x x x 14) x e x x 2 lim 15) + + x x x x x sin 1 cos 0 lim
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92.131 Calculus 1 l’Hôpital’s Rule Solutions 1) Ind. 0 0 1 1 1 1 lim 1 lim 0 0 = = = x x x x e x e 2) Ind. 0 0 1 1 1 1 cos lim sin lim 0 0 = = = x x x x x L L 3) Ind 0 0 Ind. 0 0 2 1 2 cos lim 2 sin lim cos 1 lim 0 0 2 0 = = = x x x x x x x x 4) Ind. 1 1 lim 2 2 lim 1 1 lim 2 2 = = = + x x x x x x x L L L 5) Ind. 0 lim 1 lim lim = = = x x x x x x e e e x 6) Ind. 0
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This note was uploaded on 02/13/2012 for the course MATH 92.131 taught by Professor Staff during the Fall '09 term at UMass Lowell.

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ep6 - 92.131 Calculus 1 l'Hpital's Rule Determine the...

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