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Show your work, sucka
...by the way, I get 2/15.....
Show your work, sucka
Not me...I've seen your work...but....to (find the volume of the solid whose base is the region bounded between the curves y=x, and y =x^2 and whose cross sections perpendicular to the x-axis are squares)....in order to form a 'solid' to find 'volumes' shouldn't he rotate either around the x or y axis?
Nah, that would make the cross sections washers.
To find the volume though wouldn't you make the cross-sections of the washers squares, (assuming your rotating around the y-axis)?
Since it is a square and to find the area of the square it two sides mutliplied together and since all the sides of the square are (x-x^2) it is (x-x^2)^2, and that's when you have to foil. I made the same mistake as you prior. I'm on finding arc lengths now. It's pretty tedious when they start giving you like [e^t(cost+sint)]^2+[e^t(cost-sint)]^2, that problem took a whole page.
...assuming that's true, then the answer is 2(pie)/15...
Since it is a square, it doesn't need pi, only clyinders/circles, when doing these types of problems. The answer is 1/30. You have to foil it, then integrate, then evaulate from 0 to 1.
.....maybe I'm just not seeing how those those two angles on a Cartesian plane can be squares....but if you say so....
I don't really see it either. I don't visualize problems or see how they would look graphically, I just follow the directions on how to do them.
...you have to be able to visualize math problems....wait till you get to set theory...
Set theory requires a much stronger argument than calculus does, and requires incredible careful symbol manipulation and application of axioms. Set theory is a really cool subject of study though; especially when you get around to understanding what real numbers really are. Still, (abstract) algebra and probability are my two favorite subjects.
This is what the solid from the problem looks like:
It looks the same from the side and from the top view.
The bright red is the side, the dark red is the top.
...all I remember is that it is difficult to do complex injections, surjections, and bijections without visualization.....and set theory comes right after Cal3...
..as long as we're having fun with math though....
Find the depressed cubic:
X^3 + 6X^2 + 8X = 1000
Thank god I'm not taking that. I just need Cal 1 + 2 and some stats class. I've always wondered though how it would be like to be a Math major.
Set theory for non-math majors? ZFC set theory is some pretty hairy for someone who's not a pure math major. It's certainly way too difficult for the average student to do having only done calculus up to vector spaces, linear transforms, series, and Stokes Theorem (I'm assuming that's what you mean by Cal3). You gotta have at least a class of analysis or abstract algebra to be in the kind of mindset to approach things in the axiomatic way that ZFC set theory requires.
They've broken it down to some prelim classes down here because too many people couldn't make the jump from Cal2 or Cal3 to the ZF Universe, so the very first classes focus on the axioms, set theory, the natural numbers, and then they jump to cardinality, equivalence class and relations and then into number theory and Euclidean algorithms and...yada...yada...
What's your major?
Learn how to take orders, make money, satisfy a woman, and raise kids. Everything else is just gravy.
I'm a pre-med taking my lower requirements right now (2nd semester of College so far). Organic Chemistry scares me more than Calculus 3. I guess I can tell that you are a computer science/engineer major.
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