Hi all,(adsbygoogle = window.adsbygoogle || []).push({});

My girlfriend asked me this question just now, however I have no idea how I should approach to solve it, I highly appreciate if anyone could shed lights on this:

lim x^2 times cos^2(x^-2)

x->0

I tried using the squeeze theorem:

-1 < cos(1/x) < 1

thus:

-x^2 < x^2 (cos(1/x)) < x^2

or

-x^2 cos(1/x) < x^2 (cos^2(x^-2)) < x^2 cos(1/x)

Therefore, as x->0 in the middle, the two sides also approach 0.

But I don't think it makes any sense... since 1/x as x-> 0 cannot really be used as part of the intervals representing -1 and 1.

I also tried rearranging cos^2 (x^-2), but I don't think it's any use.

Please enlighten on this, thanks in advance.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Having trouble finding this limit

Loading...

**Physics Forums | Science Articles, Homework Help, Discussion**