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Answer to Question #18375 in Real Analysis for Matthew Lind

Question #18375
Using the definition of the limit at infinity verify that
0 does not equal lim x-->infinity cosx.
Expert's answer
As we know, for any sequence xnwhich converges to infinity, cos(xn) should converge to 0 if it's a limit for
cosx. But if we consider the following sequences xn1=pi*n1 and xn2=pi/2+2*pi*n2
we get lim cos(xn1)=1 and lim cos(xn2)=0 1!=0. So 0 does not equal lim cosx
x-->infinity.

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