l'hospitals rule:
if the limit is in indeterminate form, you use this.
you take the derivative of the top and the bottom of the fraction (separately, do not use quotient rule) and then take the limit of it again.
if you get indeterminate form, repeat as many times as necessary.
this week in calc, we just went over all the ways to integrate pretty much. partial fractions, trig sub, all that good stuff. and we had a test on thursday. and now we have a take home test due this week sometime (i think either thursday/friday) if someone knows when it is due please tell me.
i'm just gonna kinda review randomness today.
sorry if it's short. i'm not really focused too well right now...
partial fractions:
whenever you simplify the bottom of the fraction as much as you can... if you have something like this n/n(n-1)
you'd use the normal rules and just do A/n + B/n-1.
but if you ever have something left in the bottom that is still squared, that's when the rules get tricky.
if your exponent is on the outside of the equation...(example: x/(x-1)^2) then you would do A/(x-1) + B/(x-1)^2
and if your exponent was 7, then you would go all the way up to 7.
no if your exponent is on the inside of the equation....(x/(x^2-1) then you would do like this... A + Bx/(x^2-1)
get it ? hopefully you do.
now i am confused on what convergent and divergent is and how you can tell the difference.
help?
Subscribe to:
Post Comments (Atom)
Convergent is if it goes to a number, and divergent is the opposite. So if I was to take the lim as x approaches inf. of 4x/x^2. the degree of the top is less than the degree of the bottom, so, you get zero right? so the function converges to 0. the only time it'll diverge is if it has an infinity somewhere.
ReplyDeleteHope this helps