SOLUTION: 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?

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(52803) (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.

-------------

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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