Question 989818
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Move *[tex \Large \cos\left(\frac{2}{x}\right)] into the numerator of the rational function factor.


Then use the fact that the limit of a quotient is the quotient of the limits of the numerator and denominator.  The denominator limit is trivial, but you will have to use the Squeeze Theorem for the numerator.


Note that *[tex \Large -1\ \leq\ \cos\left(\frac{2}{x}\right)\ \leq\ 1]  therefore *[tex \Large -x^2\ \leq\ x^2\cos\left(\frac{2}{x}\right)\ \leq\ x^2]


Hence your numerator limit is the meat on a sandwich made out of zero bread.


John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it

*[tex \Large \ \
*[tex \LARGE \ \ \ \ \ \ \ \ \ \