- #1
Saladsamurai
- 3,020
- 7
Homework Statement
Prove the Limit Statement
[tex]\lim_{x\rightarrow9}\sqrt{x-5}=2[/tex]
Okay then
I am going through the synthetic 'chicken scratch' stage of the proof here to determine a suitable guess for what [itex]\delta \text{ might be if givem some }\epsilon[/itex].
I have arrived at:
[tex]-\epsilon<\sqrt{x-5}-2<\epsilon[/tex]
[tex](2-\epsilon)^2+5<x<(2-\epsilon)^2+5[/tex]
[tex]\therefore[/tex]
[tex](2-\epsilon)^2-4<x-x_o<(2+\epsilon)^2-4[/tex]
Just wondering, should I assume that [itex]\epsilon<2[/itex]?
Is that okay to do?
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