<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>