Question

Can someone show me how to solve:
lim xcos(1/x)
x--> 0

Answer 1

cosine is stuck between \(-1\) and \(1\) but \(x\to 0\)

Answer 2

so the whole thing must go to zero
cosine can't mess it up any, as it is bounded above and below

Answer 3

@bobobobobb can you get him? me not

Answer 4

Yes @satellite73 can you explain it ?

Answer 5

can i explain what?

Answer 6

i understand it now

Answer 7

i suppose your math teacher would be happier if you used the "squeeze" theorem
\[-1\leq \cos(\frac{1}{x})\leq 1\] so
\[-x\leq x\cos(\frac{1}{x})\leq x\]

Answer 8

the limit on the left and right is clearly 0 so the limit in the middle must be 0 as well

Answer 9

thanks:)