CalcNotes0207-page6

CalcNotes0207-page6 - (Section 2.7: Precise Definitions of...

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(Section 2.7: Precise Definitions of Limits) 2.7.6 How Do We Formally Prove the Limit Statement in Part A? Prove: lim x ± 4 7 ² 1 2 x ³ ´ µ · ¸ = 5 . We have: a = 4 , fx () = 7 ± 1 2 x , and L = 5 . We need to show: ± ² > 0 , ± > 0 ± 0 < x ± a < ³ ± L < ´ ; i.e., ± > 0 , ± > 0 ± 0 < x ± 4 < ³ 7 ± 1 2 x ´ µ · ¸ ¹ ± 5 < º ´ µ · ¸ ¹ . Rewrite ± L in terms of x ± a ; here, x ± 4 : ± L = 7 ± 1 2 x ² ³ ´ µ · ± 5 = ± 1 2 x + 2 Factor out ± 1 2 , the coefficient of x . To divide the
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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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