Prove the following limit. lim, (3x-7)=14 *→7 SOLUTION 1. Preliminary analysis of the problem (guessing a value for 8).

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Prove The Following Limit Lim 3x 7 14 7 Solution 1 Preliminary Analysis Of The Problem Guessing A Value For 8 1 (20.14 KiB) Viewed 10 times

Prove the following limit. lim, (3x-7)=14 *→7 SOLUTION 1. Preliminary analysis of the problem (guessing a value for 8). Let e be a given positive number. We want to find a number & such that if 0<x-71<& then (3x-2)-141 < But 1(x-7) - 141-13x-211 - 3 Therefore, we want & such that that is, 0< x-71 <& then if 0 < x-71 < & then This suggests that we should choose - 4 2. Proof (showing that & works). Given > 0, choose & 1(x-7)-141- <36 Thus, it 0x71<&then (3x-7) - 141 Therefore, by the definition of a limit, we get the following lim, (x-7)=14 < <d, then we get the following.