CalcNotes0203-page19

CalcNotes0203-page19 - (Section 2.3: Limits and Infinity I)...

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(Section 2.3: Limits and Infinity I) 2.3.19 Example 14 Evaluate lim x ±² fx () , where = x 2 ± 3 x 3 + 4 x 2 + 1 . Solution 1 (A Rigorous Solution) : Left to the reader! Refer to Example 13. Solution 2 (The “Short Cut”: Dominant Term Substitution) lim x = lim x x 2 ³ 3 x 3 + 4 x 2 + 1 Indeterminate Limit Form ² ² ´ µ · ¸ ¹ = lim x x 2 x 3 = lim x 1 x Limit Form 1 ² ´ µ · ¸ ¹ = 0 “Super Short Cut” : This is because the numerator, x 2 ± 3 , has a degree (i.e., 2) that is less than the degree (i.e., 3) of the denominator,
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