# 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.

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.

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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