Recent content by wvcaudill2

1. Thermo Concept Questions

Homework Statement Hey, I was wondering if I could get some help verifying my answers for these general thermodynamics concept questions. Thanks! 1. A reversible reaction is at equilibrium at constant pressure and temperature if the free energy of the system ______________. 2. Heat...
2. Basic limit involving absolute value

Im still not seeing the big picture here. Can you write out exactly what this problem should look like with all the steps at least partially worked out?
3. Basic limit involving absolute value

Ok, I see what you are saying now, but when I graphed the parabola, I also saw that coming from the right-hand side, the values of x were also positive up until x=1.
4. Basic limit involving absolute value

Im still not sure how it is you are coming to the statement that "if x comes from the left, then this expression is positive." Can you explain how you are getting this? Here is what I have now:

6. Basic limit involving absolute value

I do not see how they should be switched. Can you explain your process in more detail?
7. Basic limit involving absolute value

Ok, from the left-hand side of the limit, I got -2, and from the right-hand side I got 2, and when x-1=0 I got "does not exist." Is this right?
8. Basic limit involving absolute value

Homework Statement lim as x\rightarrow-1 = \frac{|x^{2}-1|}{x^{2}+x} Homework Equations N/a The Attempt at a Solution Tried to write this as a piecewise function, but I got lost.
9. Integration by parts & inv. trig fxn

Oh, ok. Thanks again!
10. Integration by parts & inv. trig fxn

I still dont see how this gets (1/8), and even then, what is the purpose of doing this, and where does the (2x) come from?
11. Integration by parts & inv. trig fxn

Homework Statement \int xarcsin2xdx 2. The attempt at a solution Can someone explain to me what is happening at step 2? I understand how the integration by parts was done, but where does the (1/8) or (2x) come from?
12. Applying Integration by Parts & Trig Substitution

Okay, I got it now. Thanks for all your help!
13. Applying Integration by Parts & Trig Substitution

Okay, thats what I thought you wanted me to do. I am now left with this: (7/4)\int sec^{3}Θ = (3/4)secΘtanΘ - (3/4)ln\left|secΘ + tanΘ\right| + C Now I need to manipulate the fraction so as to get (4/3)\int sec^{3}Θ How do I do this?
14. Applying Integration by Parts & Trig Substitution

I am still not seeing it. Currently, I have \int sec^{3}Θ = (3/4)(secΘtanΘ - \int tan^{2}ΘsecΘ)
15. Applying Integration by Parts & Trig Substitution

Is there anyone that can help me finish this problem?