Question 1176110: Use this to compute the following limit.
x+2<= f(x) <= x^2-x+3
lim f(x)
x-->1
What theorem did you use to arrive at your answer?
Answer by ikleyn(52802)   (Show Source):
You can put this solution on YOUR website! .
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.
Solved, answered, explained and completed.
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About this referred REMARCABLE theorem, see this 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.
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