Another calculus quandry.

[Shoeberto]

This one's about to make me crazy. I don't know what I'm missing.

It's the limit as x approaches infinite of x*tan(1/x). Graphing it shows that it should approach the same thing as tan(1), and obviously getting tan(x/x)=tan(1). But I can't for the life of me seem to find any property that lets me just go to that step, and expanding the equation into sines and cosines just ends up with the whole thing coming out to 0. Helps, please.

[Shoeberto]

Nevermiiiind.

Yahoo answers got it for me.

[Peegee]

mind poasting the 'proof' so I don't have to ask my friend and have him go 'sigh I taught you this a year ago' ? :D

[Weimar Pluto Knight VII]

lim (x*tan(1/x)) = lim (tan(1/x) / (1/x)) by L'Hospital's Rule = lim ((sec (1/x))^2) * (1/x^2)/(1/x^2) = lim (sec(1/x))^2 = 1.