CalcNotes0207-page1

CalcNotes0207-page1 - (Section 2.7: Precise Definitions of...

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(Section 2.7: Precise Definitions of Limits) 2.7.1 SECTION 2.7: PRECISE DEFINITIONS OF LIMITS PART A: AN EXAMPLE We will formally prove that: lim x ± 4 7 ² 1 2 x ³ ´ µ · ¸ = 5 . The statement is of the form lim x ± a fx () = L , where = 7 ± 1 2 x , a = 4 , and L = 5 . (Figure 2.7.a) The informal idea is that, as x “approaches” or “gets closer to” 4, “approaches” or “gets closer to” 5. This informal approach represents a “dynamic” view of limits. (See Footnote 2 in Section 2.1.) The precise approach takes on a more “static” view. The idea is that, if
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