SOLUTION: Find limit(x goes towards 0) [xsin(1/x)] ? I know the answer should be 0 but am unsure of how to get that. I also know that limit(x goes towards 0) sinx/x = 1, but am not sure

Algebra ->  Test -> SOLUTION: Find limit(x goes towards 0) [xsin(1/x)] ? I know the answer should be 0 but am unsure of how to get that. I also know that limit(x goes towards 0) sinx/x = 1, but am not sure      Log On


   

Question 775765: Find limit(x goes towards 0) [xsin(1/x)] ?
I know the answer should be 0 but am unsure of how to get that. I also know that limit(x goes towards 0) sinx/x = 1, but am not sure if that helps in this question?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
-1%3C=sin%281%2Fx%29%3C=1 for all x%3C%3E0
or
abs%28sin%281%2Fx%29%29%3C=1 for all x%3C%3E0
multiplying both sides times abs%28x%29 we get
abs%28x%2Asin%281%2Fx%29%29=abs%28x%29%2Aabs%28sin%281%2Fx%29%29%3C=abs%28x%29
Since
system%28lim%28+x-%3E0%2C+%28x%29+%29=0%2Cabs%28x%2Asin%281%2Fx%29%29%3C=abs%28x%29%29
then
lim%28+x-%3E0%2C+%28x%2Asin%281%2Fx%29%29+%29=0