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Chapter 1: Q. 69 (page 108)

Prove each of the limit statements in Exercises67鈥�72. You

will have to bound 未.

limx鈫�5x2-6x+7=2

Short Answer

Expert verified

The given limitlimx鈫�5x2-6x+7=2is proved.

Step by step solution

01

Step 1. Given information. 

We are given,

limx鈫�5x2-6x+7=2

02

Step 2. Proving the limit 

Given 蔚>0, choose 未=min1,蔚5.

Then if 0<|x-5|<未, we have,

x2-6x+7-2=x2-6x+5=|x(x-5)-1(x-5)|=|(x-5)(x-1)|=|x-5||x-1|<未|x-1|

03

Step 3. Proving the limit 

Now from, 0<|x-5|<未,

x-5<1x<1+5x<6

Therefore,

<未|6-1|鈮�未(5)鈮�蔚55鈮�蔚

Hence Proved.

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