(Section 2.7: Precise Definitions of Limits) 2.7.1 SECTION 2.7: PRECISE DEFINITIONS OF LIMITSPART A: AN EXAMPLEWe will formally prove that: limx±47²12x³´µ¶·¸=5. The statement is of the form limx±afx()=L, where =7±12x, 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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