Question 1122070
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Squeeze Theorem.


Let *[tex \LARGE I] be an interval containing the point *[tex \LARGE a] and let g, f, and h be functions defined on I except possibly at a.


If


*[tex \LARGE g(x)\ \leq\ f(x)\ \leq\ h(x)\ \forall\ x\ \in I\ |\ x\ \not=\ a]


and


*[tex \LARGE \lim_{x\right{a}}\,g(x)\ =\ \lim_{x\right{a}}\,h(x)\ =\ L]


then


*[tex \LARGE \lim_{x\right{a}}\,f(x)\ =\ L]


So you need to evaluate


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \lim_{x\right{-1}}\,-x^2\ -\ 2x\ -\ 4]


and


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \lim_{x\right{-1}}\,x^2\ +\ 2x\ -\ 2]


If they evaluate to the same number, then that number is


*[tex \LARGE \lim_{x\right{-1}}\,f(x)].


If not,


*[tex \LARGE \lim_{x\right{-1}}\,f(x)]


cannot be computed from the given information.
								
								
John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it
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