Prove the following limit. lim (2x - 2) = 6 SOLUTION 1. Preliminary analysis of the problem (guessing a value for 6). Le

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Prove The Following Limit Lim 2x 2 6 Solution 1 Preliminary Analysis Of The Problem Guessing A Value For 6 Le 1 (19.57 KiB) Viewed 12 times

Prove the following limit. lim (2x - 2) = 6 SOLUTION 1. Preliminary analysis of the problem (guessing a value for 6). Let e be a given positive number. We want to find a number & such that if 0 < x-41 <& then 1(2x-2) - 61 < E Therefore, we want & such that But 1(2x-2)-61-12x-81-2 that is, if 0 < 1x-41 < 8 then 2 4 2. Proof (showing that & works). Given > 0, choose &=If 0 < 1(2x-2)-61 then This suggests that we should choose & -2 < 20 Thus, if 01x41 < & then 1(2x-2)-61 <. Therefore, by the definition of a limit, we get the following. lim (2x - 2) = 6 CF <3, then we get the following.