<p>Do we have to know washer AND shell method?
I only know one method (and I don’t even know which one that is).</p>
<p>Washer is the one where you square outer radius and inner radius and subtract them.
Shell is where you take parallel representative rectangles to the axis of revolution and solve. AB doesn’t require Shell, I believe.</p>
<p>soooooooo volume…
if rotated around the x axis or a y=n
then use (pi)integral(top curve^2-bottom curve^2) from a to be right?
and if rotated around y axis then you use
(2pi)integral of (x times height) from a to be</p>
<p>Can someone explain the Mean Value Theorem to me please?</p>
<p>If f is diff & cont on [a, b], there is a ‘c’ in [a,b] such that:</p>
<p>f’(c) = [f(b)-f(a)] / [b - a]</p>
<p>I believe thats right…</p>
<p>mean value theorem:
on a curve f(x) pick two points, a and b
if you draw a line connecting a and b it’ll give you a slope
its just basically saying that
on the f’(x) graph there must be a point, c, that has that slope</p>
<p>so say the slope from a to b is 1/4
on the derivative graph
there has to be a point where the slope is 1/4</p>
<p>wow, you guys are doing some review in here, which is really cool! ^^</p>
<p>@Dabigdawg72 and Zens: my teacher said that the shell method’s actually not included in the curriculum (it’s even not mentioned in the book we’re using in class). mm, you can solve an axis rotational problem using either washer or shell method though, so don’t worry :).</p>
<p>arghhhh, i’m not ready for the exam tomorrow at all!!! >"< may God bless me! 
good luck to all of you!!! ;)</p>
<p>If I pass, it’ll be blind luck. I get all the concepts, but I can’t apply anything.</p>
<p>Logistics - anyone care to explain??</p>
<p>AxeBack so is the Mean Value Theorem used for determining the value of a point in an interval?</p>
<p>Sorry if this has been asked before, but how can you tell whether or not to use the avg value theorem or avg rate of change equation. Is there some clue to look for in the wording?</p>
<p>No, its used to determine the RATE OF CHANGE (i.e., derivative) of that value in the interval. Its basically the slope of the curve! If ‘b’ is your max x-value and ‘a’ is your min x-value, its basically (change in y) / (change in x).</p>
<p>Can anyone tell me if the distance traveled by a particle is the same thing as the arc length for the function with respect to the bounds.</p>
<p>
[QUOTE=Melody224]
Sorry if this has been asked before, but how can you tell whether or not to use the avg value theorem or avg rate of change equation. Is there some clue to look for in the wording?
[/quote]
</p>
<p>Yes, if they want average value, they’ll specifically SAY “compute the average value of B(x) over the interval…”, whereas for something like average rate of change, it’ll probably be in disguise like: “use the data table to estimate f’(2.8)” or something.</p>
<p>Thanks so much AxeBack!</p>
<p>haha, yeah, after doing some practice tests of Barron’s’s, i realized that i have loads of stuff to review :-s.</p>
<p>do you guys think that the root test for convergence would have a high chance to appear on the test? i haven’t done this much in class :(. and Lagrange’s remainder… can anyone explain it to me by solving this problem , please? here’s the question (it’s a multiple choice one):
“you wish to estimate e^x, over the interval |x| < 2, with an error less than 0.001. the Lagrange error term suggests that you use a Taylor polynomial at 0 with degree at least:” [answer: 10]</p>
<p>oh, and i’m stuck at another multiple choice:
“at how many points on the interval [0,π] does f(x) = 2sinx + sin4x satisfy the Mean Value Theorem?” [answer: 4]</p>
<p>thank you!</p>
<p>AxeBack so an example problem to use the MVT would be:</p>
<p>If a car is traveling at the position function of f(x)=2x^2+4 on the time interval [0,6], then the velocity of the car at t=3 is…</p>
<p>And then to solve this:</p>
<p>f(6)-f(0)/6-0
76-4/6
= 12 ft/min</p>
<p>Is that correct?</p>
<p>Are there a lot of volume problems using the disk, shell, washer method?</p>
<p>This part scares me the most, by far.</p>
<p>I’m so nervous for the test tomorrow. I reviewed a lot, but I feel like the problems are going to be really hard.
Good luck, everyone!</p>
<p>
</p>
<p>Yep, but you should do that only if it asks you to use the Mean Value Theorem.
Otherwise, you could just do:
f’(x) = 4x
f’(3) = 4(3) = 12</p>
<p>MVT problems are usually more often seen on multiple choice than free-response, and its mixed up with the other theorems to confuse you, so make sure you’re able to differentiate (no pun intended) between MVT and IVT/Rolle’s Theorems.</p>
<p>Edit: ON AN FRQ, if you’re given the equation, just take the derivative of it. If you’re given a date table / graph, use MVT!</p>