Calculus Volume 1

148

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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