Friday, February 28, 2014

How can I find the lim of (3 - x^2)/(x-3) as x approaches to 3?

To check if the function has limit, when x approaches to 3,
we'll determine the lateral limit and the value of the function in accumulation
point.


For x->3, x<3 (x approaches to 3, with values
smaller than 3)


lim (3 - x^2)/(x-3) = -6/-0 =
+infinite


For x->3, x>3 (x approaches to 3, with
values higher than 3)


lim (3 - x^2)/(x-3) = -6/+0 =
-infinite


Since the lateral limits are infinite and
different, the limit of the function does not exist if x approaches to
3.

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