<p>Yeah, my teacher barely taught series and sequences, and I realized trying to teach it to myself now is impossible.</p>
<p>I don’t know a lot about series, but I can usually figure out most of the problems involving them (that I’ve encountered, anyway). Taylor series are a ***** though. :(</p>
<p>Use the formula for the Taylor Series. Don’t overthink it.</p>
<p>Nick and Hippo and Tweetjazz, I would memorize the Taylor series and the general term for sin(x), cos(x), ln(x+1), and e^(x). You may be able to derive them but it is much much MUCH easier to memorize the formula. It also saves you a lot of time.</p>
<p>The way I remember sin(x) and cos(x) is somewhat interesting and I’ll share but bare with me.</p>
<p>on the unit circle cos=x right? well, to make an X you need two lines. Two is even so the powers of the maclaurin series for cos(x) are even. and let’s pretend that 0 is also even.</p>
<p>so, cos(x)=1 - (x^2)/2! + (x^4)/4! - (x^6)/6! + …</p>
<p>b/c x^0=1</p>
<p>on the unit circle, sin=Y and to make a capital Y, you need three lines. three is odd so the powers for sin are odd.</p>
<p>sin(x)= x - (x^3)/3! + (x^5)/5! - (x^7)/7! + …</p>
<p>you always divide by the factorial of the power and the series alternate. I thought it was clever but my calculus teacher didn’t get it. Hope it helps someone else!</p>
<p>e^x is always simple. it’s just all the powers/ the power factorial. you start at 0 and keep going.</p>
<p>so…</p>
<p>e^x= 1 + x +(x^2)/2! + (x^3)/3! + (x^4)/4! + …</p>
<p>ln(x + 1) may trip you up because there are no factorials in it. The way I think of it is that ln(x+1) has a +1 attached to the X so it’s a tricky ricky type situation. So, ln(x+1) is also a tricky ricky situation because it doesn’t have the factorials AND it starts at X because X is sexy AND it alternates. (laugh all you want, but I remember these things. :))</p>
<p>so,
ln(x + 1) = x - (x^2)/2 + (x^3)/3 - (x^4)/4 + …</p>
<p>so enjoy. and i hoped you at least got a laugh (if my awesome mind trick didn’t help you.)</p>
<p>PS Is it bad that I haven’t started studying yet?</p>
<p>Yeah, taylor and power series are a b****</p>
<p>quick question
why is the derivative of 2e^x
still 2e^x</p>
<p>i guess im having a brainfart but sohuldn’t it be just e^x… 
im dumb</p>
<p>because the derivative of e^x is always e^x
you keep the constant when you take the derivative
hence the derivative of 2x is 2</p>
<p>?</p>
<p>right >< thanks</p>
<p>for sin/cos taylor series .. you could also just memorize the sin series and do the derivative of it to get the cos taylor series 
(for both individual terms and the general term)</p>
<p>Nice idea, proud08er!</p>
<p>I took the AP stats exam today and it was hard. If the Calc BC test is supposed to be harder, then I’m scared!!! I get everything, but the questions are gonna be hard cus AP just makes it confusing! The only subject I’m a little shaky on is the lagrange error bound and the volumes of things by using cross-sections so I’m going to review those now and take a practice test. The exam is tomorrow morning !!! I hate morning tests!!</p>
<p>What percent do you need to get right on BC for a 5?</p>
<p>im winging it =D</p>
<p>bump my questions 2 up if anyone knows?</p>
<p>You have to get roughly 60% of the total composite score.</p>
<p>I’m not. :]</p>
<p>thanks crn</p>
<p>Do we have to know work? Our teacher said no, but my barrons review has the work problems like when a barrell of oil is being emptied over the top and springs being springed and stuff. But then barrons overdoes it I have heard, so work or no work?</p>
<p>I think its fair game for the MC, its just force times distance, although the distance part can get a little tricky when you’re integrating…what about Lagrange, we didn’t really cover it but I’m guessing there might be a MC about it.</p>
<p>My teacher told us that LaGrange is such a miniscule part of the test if its even on there that it won’t matter so she didn’t teach it.</p>