Question

How do I do this problem?
Find the limit: lim as x --> infinity of x * sin (1/x)=

Answer 1

let u=1/x
as x->infinity, u->0

Answer 2

limit turn out to be "1"

Answer 3

i doubt it

Answer 4

oh maybe i am wrong

Answer 5

\[
L=\lim_{u\to0}{\sin u\over u}=1
\]

Answer 6

yeah, i am wrong

Answer 7

@satellite73 :)

Answer 8

to err is human

Answer 9

How'd you get to the L equation?

Answer 10

\[u={1\over x}\\as\;x\to\infty,\;u\to0
L=\lim_{x\to\infty}x\sin\left({1\over x}\right)\\
L=\lim_{u\to0}{\sin u\over u}=1\]

Answer 11

Man I feel like an idiot, I still don't get it... Why did you put the sin u over u?

Answer 12

by the substitution

Answer 13

1/x =u
and
x=1/u

Answer 14

you see it now?

Answer 15

I guess so man... I appreciate your help, I hope this isnt on the exam lol.