On-line Math 21

1.3  Infinite Limits

Example 3

lim x® 1-  1 x-1

Hints

Here there is nothing to divide out, or simplify. What happens to the denominator as x approaches 1? What about when you keep x < 1 , which is what that x® 1- means?

Finish it

Well, the denominator is going to 0, of course, as x® 1- , but it is always negative, since x < 1 , so the fraction is very large (since the denominator is going to 0), and negative (since the denominator is negative and the numerator is positive), heading to -¥ in the limit,

lim x® 1-  1 x-1 = -¥.

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Copyright (c) 2000 by David L. Johnson.