CalcNotes0204-page4

CalcNotes0204-page4 - (Section 2.4: Limits and Infinity II)...

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(Section 2.4: Limits and Infinity II) 2.4.4 PART C: RATIONAL FUNCTIONS Example 2 (Contrast with Example 1) Evaluate lim x ± 0 + 1 x 2 , lim x ± 0 ² 1 x 2 , and lim x ± 0 1 x 2 . Solution Because x 2 > 0 for all nonzero values of x , all three give the Limit Form 1 0 + ±² . Here is the graph of y = 1 x 2 : (Figure 2.4.b) Example 3 Let fx () = x + 1 x 2 + 4 x . Evaluate lim x 4 + , lim x 4 ² , and lim x 4 . Solution Method lim x 4 x + 1 = ² 4 + 1 = ² 3 . This is also true for the one-sided variants. lim x 4 x 2 + 4 x = ² 4 2 + 4
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