Hello,(adsbygoogle = window.adsbygoogle || []).push({});

[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

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Lim x->+inf xsin(1/x)

**Physics Forums | Science Articles, Homework Help, Discussion**