# Math Help - Lhospitals rule helppleaseee...

1. All right, listen carefully, class . . .
. . (There will be a quiz later.)

. . . . . . . . . . . . . . . . 1
. . . . . . . . . . . . . . .-------
. . . . . . sec²x . . . . .cos²x . . . . . .1 . . . cos x . . . . . . . .1
I had: . ------- . = . --------- . = . ------- . ------- . = . -------------
. . . . . . tan x . . . . . sin x . . . . .cos²x . .sin x . . . . .sin x cos x
. . . . . . . . . . . . . . .-------
. . . . . . . . . . . . . . . cos x

2. Originally Posted by Soroban
All right, listen carefully, class . . .
. . (There will be a quiz later.)

. . . . . . . . . . . . . . . . 1
. . . . . . . . . . . . . . .-------
. . . . . . sec²x . . . . .cos²x . . . . . .1 . . . cos x . . . . . . . .1
I had: . ------- . = . --------- . = . ------- . ------- . = . -------------
. . . . . . tan x . . . . . sin x . . . . .cos²x . .sin x . . . . .sin x cos x
. . . . . . . . . . . . . . .-------
. . . . . . . . . . . . . . . cos x
Yes, Soroban, we have established that your algebra is correct (see the top of this page). The issue is that the function will still be undefined at pi/2

3. 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).

4. Originally Posted by ^_^Engineer_Adam^_^
The last link shows that the limit is lim(x -> pi/2)(-tan(x)) which is undefined. This is correct. You can't apply L'Hopital's rule again because you don't have a 0/0 situation.

-Dan

5. 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!)

6. Originally Posted by ThePerfectHacker
the Riemann hypothesis should be named after me!
Ha!

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