CalcNotes0203-page7 - (Section 2.3: Limits and Infinity I)...

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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 . 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 x 1 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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