Recent content by ravenea

In the order drdzdtheta, i get: 0 <= theta <= 2pi sqrt(z^2 + 3)/2 <= r <= sqrt(2-z^2) -1 <= z <= 1 I understand your point, the radius varies from z = -1 to z = 1 because of the hyperboloid, but the exercise is asking me to give the integrals for both orders: dzdrdtheta, drdzdtheta Thanks for...

Homework Statement I need to calculate the integral where the region is given by the inside of x^2 + y^2 + z^2 = 2 and outside of 4x^2 + 4y^2 - z^2 = 3 Homework Equations The Attempt at a Solution So far, I think that in cylindrical coordinates (dzdrdtheta): 0 <= theta <= 2pi sqrt(3)/2 <=...

Homework Statement Integral of (ln(e^x + 1))^(1/3) / (e^x + 1) See http://www2.wolframalpha.com/input/?i=integral+of+%28ln%28e**x+%2B+1%29%29**%281%2F3%29%2F%28e**x+%2B+1%29"Homework Equations N/A The Attempt at a Solution First, substitute k = ln(e^x + 1) dk = dx(e^x)/(e^x + 1) Then, used...

Ok, so there would be 5 - 2 = 3 ways to sit them around, and that gives us 3 * C(8, 4) = 210. Thanks!

Ok, using what you said in post #7 I can see where the answer comes from. However I still don't understand how to solve it as you suggest in post #6. My guess is that one can sit the enemies in 2! different ways. Can you please explain me how you did it?

First of all, thanks for your help! So after giving it some more thought, I finally got to see my mistakes and how to fix them. However, I still cannot solve the e). My new answers: e) I still do not get this one. f) Total ways of seating everyone: C(8, 4) * (6 - 1)! = 8400. Total ways of...

They are always sitted.

Hi everyone, I want to make sure if I solved this problem correctly. Thanks in advance. Homework Statement Rachel invited her friends to dinner. She has 10 friends, but only 6 places to sit them in her (circular) table. a) Count the ways to sit the guests if order is not important. b) If...

I want to know if it is correct. What worries me is if I can state that -1 \leq \sin{\frac{\pi}{x}} \leq 1 since x is approaching 0, and right there \frac{\pi}{x} is undefined. Thanks in advance.

Homework Statement \lim_{x \to 0} \sqrt{x^3 + x^2}\sin\frac{\pi}{x} Homework Equations The Attempt at a Solution We know that -1 \leq \sin\frac{\pi}{x} \leq 1 \Leftrightarrow -\sqrt{x^3 + x^2} \leq \sqrt{x^3 + x^2}\sin\frac{\pi}{x} \leq \sqrt{x^3 + x^2} since \sqrt{y} \geq...