• January 21st 2010, 06:28 PM
Lord Darkin
Can someone double-check my work here? Thanks, if you can. (Nod)

$
\lim_{x\to\infty}[x(1-cos(1/x))]
$

Put x to the denominator to use L'Hopital's rule, etc. Applied chain rules, etc.

$
\lim_{x\to\infty}[sin(1/x)]
$

Thus, if x goes to infinity, the above is sin(0) = 0. Final Answer: Zero
• January 21st 2010, 06:35 PM
Krizalid
Yes, it's okay, but you don't need that rule, you can turn that limit into a known one with a simple substitution.
• January 22nd 2010, 12:39 PM
Lord Darkin
Oh, really? What is this substitution? :)
• January 22nd 2010, 12:39 PM
Krizalid
$t=\frac1x.$
• January 23rd 2010, 03:58 AM
Seulementrien
tx=1

so itequals to lim [(1-cost)/t]
t->0