Question

Prove that the lim x ->0 xcos(1/x) = 0 Prove that the lim x ->0 xcos(1/x) = 0 @Mathematics

Answer 1

By the squeeze theorem\[0\le \lim_{x \rightarrow 0}\cos(1/x)\le1\]\[\lim_{x \rightarrow 0} (x \times 0)\le \lim_{x \rightarrow 0}xcos(1/x)\le \lim_{x \rightarrow 0}x\]\[0\le \lim_{x \rightarrow 0}xcos(1/x) \le 0\]therefore\[\lim_{x \rightarrow 0} xcos(1/x) = 0\]

Answer 2

thnks I used -1 <= cos(1/x) <=1
-x <= xcos(1/x) <=x
lim (-x) = 0 and lim x = 0

Answer 3

o whoops yea that should be a -1

Answer 4

cool but the squueze thm is the way to go thnks for confirming,