CalcNotes0205-page4

CalcNotes0205-page4 - (Section 2.5 The Indeterminate Forms 0/0 and 2.5.4 Example 1(Factoring and Canceling Dividing x2 1 Evaluate a lim f x and b

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(Section 2.5: The Indeterminate Forms 0/0 and ± / ± ) 2.5.4 Example 1 (Factoring and Canceling / Dividing) Assume fx () = x 2 ± 1 x 2 ± x . Evaluate: a) lim x ± 1 , and b) lim x ± 0 . Solution to a) lim x ± 1 = lim x ± 1 x 2 ² 1 x 2 ² x Limit Form 0 0 ; x ² 1 is a common factor ³ ´ µ · ¸ = lim x ± 1 x + 1 = lim x ± 1 x + 1 x = 1 + 1 1 Warning 1 : Don't remove lim x ± 1 until this substitution and evaluation phase. ³ ´ µ · ¸ = 2 Commentary on a) • We see that: x 2 ± 1 x 2 ± x = x + 1 x x ² 1 . Therefore, lim x ± 1 x 2 ² 1 x 2 ² x = lim x ± 1 x + 1 x . See Section 2.1, Part C on the “Ignore a ” Theorems. lim
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This note was uploaded on 12/29/2011 for the course MATH 150 taught by Professor Sturst during the Fall '10 term at SUNY Stony Brook.

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