Limit Help

[arianizadi]

I can't seem to find anything online about this or maybe I am not searching for it correctly but here it is...

If the Lim as x approaches 2 of (f(x) - 2) / (x - 3) = 2 then what is the Lim as x approaches 2 of f(x)?

 

[Deleted member 4993]

I can't seem to find anything online about this or maybe I am not searching for it correctly but here it is...

If the Lim as x approaches 2 of (f(x) - 2) / (x - 3) = 2 then what is the Lim as x approaches 2 of f(x)?

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[Steven G]

Just plug in 2 for x and then solve for f(2). That value will be your limit. Now show us your work.

 

[pka]

I can't seem to find anything online about this or maybe I am not searching for it correctly but here it is... If the Lim as x approaches 2 of (f(x) - 2) / (x - 3) = 2 then what is the Lim as x approaches 2 of f(x)?

Suppose that \(\displaystyle \mathop {\lim }\limits_{x \to 2} f(x) = L\)

\(\displaystyle \begin{gathered}
\mathop {\lim }\limits_{x \to 2} \frac{{(f(x) - 2)}}{{(x - 3)}} = \frac{{L - 2}}{{ - 1}} = 2 \hfill \\
\Rightarrow L = 0 \hfill \\ \end{gathered} \)
Please note that we do not know that \(\displaystyle \bf f(2)=L\), but by the given we know that the limit exists.