SOLUTION: Show that {{{(lim)x->0}}} {{{ ((x^2)/(x^2+9))cos(2/x) }}} exists. Please show the steps needed in order to solve. Thank you

Question 989818: Show that exists. Please show the steps needed in order to solve.
Thank you
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

Move

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

therefore

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

John

My calculator said it, I believe it, that settles it

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