Bounded Definition and 514 Threads

There are two problems I got stuck... 1. Is the area in the first quadrant bounded between the x-axis and the curve \ y= \frac{x} {2*(x^2+2)^{7/8}} finite? This one, I used the Area formula... but then I cannot integrate it... and then how to determine if it's finite or not? 2...

[FONT=Arial]The homework question is this: Prove If D is a bounded subset of R then D bar = D U D’ is also bounded where D’ is the set of accumulation points of D. What is a general outline of a proof?

Here is the problem: First Part (already done): Find the volume of the solid that is bounded above by the cylinder z = 4 - x^2, on the sides by the cylinder x^2 + y^2 = 4, and below by the xy-plane. Answer: \int_{-2}^{2}\int_{-\sqrt{4 - x^2}}^{\sqrt{4 - x^2}}\int_{0}^{4 -...

Here is the problem: Find the volume of the solid that is bounded above by the cylinder z = 4 - x^2, on the sides by the cylinder x^2 + y^2 = 4, and below by the xy-plane. Here is what I have: \int_{-2}^{2}\int_{-\sqrt{4 - x^2}}^{\sqrt{4 - x^2}}\int_{0}^{4 - x^2}\;dz\;dy\;dx\;=\;12\pi...

Evaluate the integral over the bounded closed region B \int \int_{B} x^2 y^3 dx dy B is the region bounded by y=x^2 and y =x certainly the x=0 to x=1 will be the limits for the x part but what about the y does it go from root y to y? please help! i neeed to understand how to setup...

Find the area of the region bounded by: r= 6-2sin(\theta) here's what i did: 6-2sin(\theta) = 0 sin(\theta) = 1/3 so the bounds are from arcsin(-1/3) to arcsin(1/3) right? my integral: \int_{-.339}^{.339} 1/2*(6-2sin(\theta))^2 i get a answer of 0.6851040673*10^11, and it's...

How do I do this problem below? Plz guide me step by step or a least show me the correct bounds so I can learn...thanks ***Find the area bounded by y^2=x and y=x=2 Thanks so much

problem: find volume bordered by cylinder x^2 + y^2 = 4 and y+z=4 and z=4. the answer is said to be 16p. but I couldn't find it. I found it in double integral part.so it must be solved with double integral. I tried with Jacobian tranformation. nut still couldn't solve it. I was confused...

Find the area bounded by the two curves: x=100000(5*sqrt(y)-1) x=100000(\frac{(5*sqrt(y)-1)}{(4*sqrt(y))}) i'm having a lot of trouble trying to find the lower and upper limit of the two functions. I tried setting the two functions together and solving for y, but i get 0. then trying to...

could someone give me an example of a function that is bounded but is nonintegrable? i need to know what a nonintegrable function bounded on [a,b] is as said in my preperation file for a test? urgent help needed

If A is a bounded subset of the reals, show that the points infA, supA belong to the closure A*. At first the answer seems obvious to me since A* contains its limit points. I'm just having trouble putting it into words, any suggestions would be great, thanks.

This is the problem: find the area of the region bounded by the curves f(x) = x^2 + 2 and g(x) = 4 - x^2 on the interval [-2,2] I did the whole integral from -2 to 2 with (4-x^2) - (x^2 + 2) dx because the graph of g(x) is on top between the region bounded. But from my drawing, the points...

Can someone please help me w/ these problems below: Find the volume generated by revolving the area abounded by x=y^2 and x=4 about a)the line y=2 b)the line x= -1 ***I tried to write out the integral not sure if it's correct: a) V=pi* int. of (sqrt(x)^2-(2-sqrt(x))^2) dx **integral form...

I don't know if anyone will be able to help me, I am really stuck on this question! "Show that the volume of the region bounded by the cone z=sqrt((x*x)+(y*y)) and the parabloid z=(x*x)+(y*y) is PI/6" The bits in the brackets (ie x*x and y*y) are x squared and y squared respectively and...