Hello, could someone please help me out with the following question?(adsbygoogle = window.adsbygoogle || []).push({});

Q. Find the limit [tex]\mathop {\lim }\limits_{x \to 2} \left( {\frac{{2x - 1}}{{x + 1}}} \right)[/tex] and verify the result by [tex]\varepsilon - \delta [/tex] argument.

I got the limit as 1 so I began to look for a value of delta.

Required: [tex]\left| {\frac{{2x - 1}}{{x + 1}} - 1} \right| < \varepsilon [/tex] whenever [tex]0 < \left| {x - 2} \right| < \delta [/tex].

[tex]\left| {\frac{{x - 2}}{{x + 1}}} \right| < \varepsilon[/tex] whenever [tex]0 < \left| {x - 2} \right| < \delta [/tex].

I get stuck at this point. Even after I use division on the LHS I still don't get anywhere. Perhaps I need to consider values of x near 2 and deduce something from that? I dunno. Could someone please help me out? Any help would be great thanks.

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# Homework Help: Look for a value of delta limit

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