CalcNotes0207-page10

CalcNotes0207-page10 - (Section 2.7: Precise Definitions of...

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(Section 2.7: Precise Definitions of Limits) 2.7.10. How Does the Static Approach to lim x ±² fx () = L Meld with the Dynamic Approach? Why is lim x 1 x + 2 ³ ´ µ · ¸ = 2 ? Because, regardless of how small we make the tolerance level ± and how tight we make the lottery for the players, there is a “point of no return” M after which all the players win; in other words, the corresponding shaded region traps the graph of f . As ² 0 + , we can choose values for M in such a way that the shaded region always traps the graph and zooms in, or collapses in, on the HA
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