- #1
fishingspree2
- 139
- 0
Hello,
[tex]\[
\mathop {\lim }\limits_{x \to + \infty } x\sin ({\textstyle{1 \over x}})
\]
[/tex]
In my textbook they show a way to do this limit using variable substitution. I understand how they did it,
however, before I saw what they did, I tryed to work it out intuitively... as x goes to infinity, 1/x goes to 0... since sin(0) = 0, then the limit must be equal to 0
the correct answer is 1, but I don't understand why the intuitive method fails. can somebody help me out?
thank you, sorry for bad english
[tex]\[
\mathop {\lim }\limits_{x \to + \infty } x\sin ({\textstyle{1 \over x}})
\]
[/tex]
In my textbook they show a way to do this limit using variable substitution. I understand how they did it,
however, before I saw what they did, I tryed to work it out intuitively... as x goes to infinity, 1/x goes to 0... since sin(0) = 0, then the limit must be equal to 0
the correct answer is 1, but I don't understand why the intuitive method fails. can somebody help me out?
thank you, sorry for bad english