Using the definition of the limit at infinity, verify that
0 does not equal the limit x-->infinity cosx.
1
Expert's answer
2012-11-14T07:24:55-0500
By definition, y0 is a limit off x-->x0 when for any xn-->x0 f(xn)-->y0. now we pick two sequences xn1=2pi*n1 xn1-->infinity cos(xn1)=1 for any n1. xn2=pi/2+2pi*n2, xn2-->infinity, but cos(xn2)=0. contradiction.
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