Question #4301d

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Answer 1 · 2017-01-23T01:49:17

See below.

Here is my attempt to explain what the question is:

Given that

#2x-1 <= f(x) <= x^2-2x+3# for all #x != 2#,

find #lim_(xrarr2)f(x)#.

If this is correct then we will use the squeeze theorem (a.k.a. the sandwich or pinch theorem).

Note that

#lim_(xrarr2)(2x-1) = 4-1 = 3#

and

#lim_(xrarr2)(x^2-2x+3) = 4-4+3 = 3#.

Therefore,
#lim_(xrarr2)f(x) = 3#.