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Chapter 2 | Limits
Figure 2.19 The graph of f ( x ) =1/ x confirms that the limit as x approaches 0 does not exist.
2.8 Evaluate each of the following limits, if possible. Use a table of functional values and graph f ( x ) =1/ x 2 to confirm your conclusion.
1 x 2 1 x 2
lim x →0 −
a.
lim x →0 +
b.
1 x 2
c. lim x →0
It is useful to point out that functions of the form f ( x ) =1/( x − a ) n , where n is a positive integer, have infinite limits as x approaches a from either the left or right ( Figure 2.20 ). These limits are summarized in Infinite Limits from Positive Integers .
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