<p>Here is the list of topics you will be tested over: </p>
<p>Limits
Continuity
Derivatives/slopes
Rules for differentiation
implicit differentiation
Mean value theorem
Max/mins
related rates
parametrics
trig functions
Deriving lnx, e^x, logs...
Inverse derivatives
Differential equations
seperating variables
euler's method
slope fields
u substitution
area under curve
riemann sums
fundamental theorems of calc
area b/w 2 curves
solids of revolution
integration by parts
inverse trig functions
partial fractions
improper integrals
polar equations
Series/sums
series tests</p>
<p>This is basically teh table of contents from the PR book (for those that don't have it)...</p>
<p>Ok......for review....Answer the question in the previous post AND ask your own question, i'm sure you guys have seen this in other review threads...So here we go:</p>
<p>Under what circumstances is the Mean value theorem valid for the interval [a, b]?</p>
<p>Function must be continuous on [a, b] and differentiable on (a, b). I think that is what you were looking for.</p>
<p>What is the absolute maximum value of the function y = 2x /( x^2 + 16)?</p>
<p>go on room: apcalcbc on AIM.</p>
<p>I'm 2 lazy to answer the question, but the instructions:
take the derivative, set it to 0 and solve for x, find out if at that point, y' goes from + --> - or vice versa. Max is positive to negative.</p>
<p>can someone show me ho to do this problem
the integral of (sin^4x dx)
i can’t seem to get the hang of it…:(</p>
<p>integration by parts with sin^2x as u and dv</p>
<p>when it comes to parametric equations,</p>
<p>what is the difference between
(dy/dt)/(dx/dt)
and
((dy/dt)^2+(dx/dt)^2)^(1/2)??</p>
<p>I know the first is dy/dx and the second is the velocity vector…but when do I used which?</p>
<p>And when it comes to polar equations,</p>
<p>when do I use (dy/d0)/(dx/d0) versus
(r prime)(sin0)+(r)(cos0) / (r prime)(cos0)-(r)(sin0)</p>
<p>??</p>
<p>i would like to know this too…:)</p>
<p>
</p>
<p>First one is the slope at the given point. Second one is the average speed at the given point.</p>
<p>Have no idea on the second question.</p>
<p>But, if they are both position curves, then isn’t the first expression velocity? And if the second expression IS velocity, then why don’t the two give one the same answer when one plugs in the same value for t?</p>
<p>^ I don’t really understand it, actually. But the second one is to find the “average speed”, so kind of like you arrive at a point, and that’s the average distance/time. The first one is just the velocity or the slope of the tangent at that pt. Yeah, if that made any sense…</p>
<p>Yeah it makes some sense. But the logic behind why they aren’t the same isn’t there (for me at least). Because one is the slope of a position curve (which is velocity) and the other is the x and y velocity vectors made into a hypotenuse to find an overall velocity. But if you use something like x=t^3+5 and y=x^2, then the velocities aren’t exactly identical. But I would have figured they would be.</p>
<p>^ Nah, it made no sense to me. I just stopped to bother with it, since I got a bunch of other stuff I need to review. </p>
<p>Here’s my question: Find the radius of convergence of Sum((x-3)^2n/n)?
How do you find it? Use the ratio test, and I get (x-3)^2 < 1, which doesn’t have a radius of 1… What did I do wrong? </p>
<p>It’s on the released practice multiple choice test-question 17.</p>
<p>Ahh help, does anyone know how to do Lagrange error bounds on Taylor series?</p>
<p>Is the answer R=3?</p>
<p>i have no idea manatee…my calc skills need some brushing up on…obviously…</p>
<p>i have a question though…for the ABC integrals…how do you know what to put for A/b??</p>
<p>And for Lagrange, I THINK it is just showing how off a finite series is versus the whole series. And basically, because the series gets smaller with each successive term, the next text is a good approximation of how for off the finite series is. So if you had the first 3 terms, the 3rd term minus the fourth term would tell you the error.</p>
<p>CORRECT ME IF I AM WRONG. I AM NOT SURE.</p>
<p>Manatee was the answer R=3?</p>
<p>The radius of convergence is 1 and the interval of convergence is 2<x<4</p>
<p>Maybe I should clarify the equation a little. It’s Sum of [ ((x-3)^(2n)) /n ]</p>