# Lect27 - Indeterminate Forms Consider the following three...

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92.131 Lecture 27 1 of 11 Ronald Brent © 2010 All rights reserved. Indeterminate Forms Consider the following three limits 1 ) x x x 2 0 lim 2 ) x x x 0 lim 3 ) 2 0 lim x x x Since 0 lim lim 2 0 0 = = x x x x , in each case we have a quotient like 0 0 , but 0 lim lim 0 2 0 = = x x x x x 1 1 lim lim 0 0 = = x x x x x x x x x 1 lim lim 0 2 0 = does not exist We call the form 0 0 indeterminate since one cannot determine what the limit will be.

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92.131 Lecture 27 2 of 11 Ronald Brent © 2010 All rights reserved. Other Indeterminate Forms 1 ) x x e x 2 lim H e r e = = x x x e x lim lim 2 so we have 2 ) x e x x 1 sin lim Here = x x e lim and 0 1 sin lim = x x so we have 0 This is called an indeterminate product
92.131 Lecture 27 3 of 11 Ronald Brent © 2010 All rights reserved. There following are indeterminate powers: 3 ) x x x 1 ) 1 ( lim 0 + + H e r e 1 ) 1 ( lim 0 = + + x x and = + x x 1 lim

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Lect27 - Indeterminate Forms Consider the following three...

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