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Unformatted text preview: (Section 2.3: Limits and Infinity I) 2.3.7 Example 6 Limit Form 1 Evaluate lim
x 3 1 , also written as lim
x x 1
x1/3 Solution Method
Observe that 1 1 as x
(See Section 2.1, Example 3; also, Example 2 in this section.)
3 as x
As x increases without bound, so does its cube root. Also, It helps to consider the graph of y = 3 x : (Figure 2.3.g)
Therefore, the Limit Form 1 applies here, and lim
3 = 0. x Solution lim x 1
3 Limit Form 1 =0 x A graph can help demonstrate (?) this.
Consider the graph of y = 1
3 : x (Figure 2.3.h)
Unfortunately, the HA at y = 0 might not have been clear in the
absence of the dashed line there. Be careful about living by
graphing calculators alone! ...
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- Fall '10