All right, listen carefully, class . . .
. . (There will be a quiz later.)
. . . . . . . . . . . . . . . . 1
. . . . . . . . . . . . . . .-------
. . . . . . sec˛x . . . . .cos˛x . . . . . .1 . . . cos x . . . . . . . .1
I had: . ------- . = . --------- . = . ------- . ------- . = . -------------
. . . . . . tan x . . . . . sin x . . . . .cos˛x . .sin x . . . . .sin x cos x
. . . . . . . . . . . . . . .-------
. . . . . . . . . . . . . . . cos x
my classmate's answers is zero
Heres how he did it
http://rogercortesi.com/eqn/tempimagedir/eqn9372.png
Applying Lhopitals rule
http://rogercortesi.com/eqn/tempimagedir/eqn4711.png
" " "
http://rogercortesi.com/eqn/tempimagedir/eqn1326.png
And lastly
I don't have time to look at his work as I have class in 10 minutes, but the limit is definitely not 0. Just look at the graph above given by THP to convince yourself of this. And since the LHL and RHL do not equal each other, the lim is undefined (globally any way).
Instead of us calling it "L'Hopital" rule, I think we should create the convention here to call it "Bernoulli's rule" for he was the one who discovered it. It just was named after somebody else (which happens all over mathematics. For example, the Riemann hypothesis should be named after me!)