<p>This is an example of the type of question I do not understand how to do.</p>
<p>Use the Derivative Form (Lagrange's Form) of the Remainder Rk(x) to determine the degree of the Taylor polynomial that is needed to calculate cos 2 to four decimal places.</p>
<p>Also, I can't figure out how do do it with the integral form of the remainder. </p>
<p>Self studying BTW, this is the first thing i cannot figure out. It scares me. </p>
<p>Thanks</p>
<p>Oh come on. Not a single person can do this? Please, I need to know this... argh.../?!?@/3$/3?</p>
<p>For those Lagrange things, don't you need to have an interval, to plug into (x-x0)? I always forget what you do when an interval isn't given...</p>
<p>well, if it is a Mclaurin series, then a=0 and x=2, but what do you do with c? I don't get it at all please help me.</p>
<p>I think a and c are the same thing?</p>
<p>If a is not given, assume that you are looking at a Mclaurin series (i.e. a=0). </p>
<p>Since we're looking for cos2 correct to 4 decimal places, x=2 and want R< .00005.</p>
<p>In this case, M=1 since derivatives of cosx are going to be + or - sinx and cosx, all of which have bounds of 1. So, according to the formula:</p>
<p>Rk(x) = 1/(k+1)! * (2-0)^(k+1)</p>
<p>At this point, use your calculator to try different values for k+1 and see how big you have to get k+1 for R to be < .00005. Here, k+1 = 12 is when that first happens. Therefore, the 12th degree polynomial will be the first omitted term.</p>
<p>Since the Taylor polynomial for cosx is 1-x^2/2!+x^4/4!... with no odd-degree polynomials, we will go up through ...-x^10/10!</p>
<p>Ans: a tenth-degree Taylor polynomial.</p>
<p>You must use the lagrange error bound formula. This is the most difficult sub-topic in Series which is the most difficult topic in all of Calc BC.</p>
<p>I still don't get it completely, but I am almost there. I'll read over it tonight and post how I did it tomorrow. Shockingly, there are very tutorials on how to do lagrange error bounds, and by the off-chance you find one, it is usually described in contorted/verbose manner which is difficult to understand. </p>
<p>Beware! it's going to be a long post.</p>
<p>snowia, you are AMAZING! THANK YOU!!! Ok, now if you would be so kind, could you post an example of the same problem, but using the integral form of the remainder? </p>
<p>Thanks for being someone who knows how to do this!!!</p>