Kay. Since I've yet to touch on L'Hopital's Rule, I shall do so now.
The most important thing to learn about l'Hôpital's rule is when it should not be used:
Definitely do NOT use it when the limits of the two parts are not both 0, or both infinity. In this case the rule is likely to give a wrong answer!
Example:
limx->0+ (cos x)/x
is positive infinity, because the numerator approaches 1 while the denominator approaches 0. If we incorrectly apply l'Hôpital's rule, we get
limx->0+ (- sin x)/1 = 0.
So you DO use L'Hopital's Rule when you get an indeterminate in the first place...this is inf/inf, 0/0, etc.
Okay, for Trig SUB!!!!! I'm getting pretty good at this, so bear with me....
My trick is: Everytime I see a trig function to an odd power, I take out an even...After this I use an appropriate identity. It's really not all that hard...I have my notecards somewhere...just ask me for them..
OkAY!!!! for things you can comment on....
Does anyone know how to:
1. Divide stuff? like x^2 + x+ 7 all over x-8. the other day BRob tried to do a problem like that, and I failedddd miserably. Easier way??
2. Chasing the Rabbit. One time I ended up with chasing the rabbit, but the answer was something super easy. any hints as to when you should use by parts i.e. chasing the rabbit?
alright. night.
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kk, malpal, i know its chasing the rabbit when there is an e and a trig function. why might you ask? because an e is always an e whether you integrate or derive it..and a trig function is always a trig function likewise!
ReplyDeletehope this helps :)
MalPal, for division like the example you just said, you use synthetic division.
ReplyDeleteSo you do your little box in the top left.
8 would be in the box because you solve the denominator for x.
Then the top line would be 1 1 7 because of you're coeffiectents. You then bring down your one and mulitply by 8, bring the 8 to the second column and the process repeats.
kk so mal, chasing the rabbit.
ReplyDeleteyou have an integral. you do by parts. and then you do by parts again. and then you end up with the exact same integral you started with. (and steph is right it usually involves a trig function and an e) then when you end up with the same thing, you just set the whole thing equal to the problem you started with.
then you put both integrals on one side, and solve.