# Limit as x tends towards +infinity for cos(1/x) to be 1

1. Dec 5, 2009

### grizz45

I have worked out the limit as x tends towards +infinity for cos(1/x) to be 1, as cos (1/infinity) would be cos(0) which is 1. However the answer in the book with the question says that the answer should be (0,3) and (3,+infinty)!!! Is this a misprint or have i gine drastically wrong?

2. Dec 5, 2009

### rasmhop

Re: Limits

Of course
$$\lim_{x \to \infty} \cos(1/x)$$
doesn't tend toward (0,3) and (3,infty) (how would that make any sense?). That is probably the answer to a different problem (have you checked the problem number and chapter number is correct?). Your idea is correct except for the fact that 1/infinity makes no sense, but since cos is continuous and defined in 0 you have:
$$\lim_{x \to \infty} 1/x = 0 \Rightarrow \lim_{x \to \infty} \cos(1/x) = \cos(0) = 1$$