Question

Prove that lim x to 0 of xsin(1/x)=0

Answer 1

You have to take the positive and the negative zero which is the right side of zero and the negative side of zero. See if those sides goes to 0, and if it does then the limit is true.

Answer 2

lim of sin(1/x) doesn't exist

Answer 3

x ---> 0

Answer 4

\[\lim_{x \rightarrow 0^+}xsin \frac{ 1 }{ x }\]AND\[\lim_{x \rightarrow x^-}xsin(\frac{ 1 }{ x })\]

Answer 5

let t=1/x

Answer 6

\[0^-\]

Answer 7

as x->0 then t->infty

Answer 8

so the limit becomes\[\lim_{t\to\infty}\frac{\sin t}t\]