Question 1176110
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<pre>

Notice that    (x+2) ---> 3    as  x ---> 1


and          (x^2-x+3) ---> 3  as  x ---> 1.



Then the theorem about two policemen is applicable, which states

that under given conditions,  lim f(x) = 3  as  x ---> 1.
</pre>


Solved, &nbsp;answered, &nbsp;explained  and completed.


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About this referred &nbsp;REMARCABLE &nbsp;theorem, &nbsp;see this &nbsp;Wikipedia article


https://en.wikipedia.org/wiki/Squeeze_theorem#:~:text=The%20story%20is%20that%20if,end%20up%20in%20the%20cell.



In different countries, in different cultures and in different cources and textbooks, this Theorem is known

under different names --- so, it is very possible that you know it under another name.