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...
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?
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.
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:
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.
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?
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?
Homework Statement
\int\sqrt{4+9x^{2}}dx
Homework Equations
Pythagorean Identities?
The Attempt at a Solution
I find it sort of cumbersome to use the special formatting here, so I hope it is okay that I just photocopied my work on paper.
You can see how far I made it, but...
Homework Statement
http://img857.imageshack.us/i/no34.jpg/ [Broken]
Homework Equations
The Fundamental Theorem of Calculus, i.e., taking the derivative of an integral yields the original function.
The Attempt at a Solution
I am not sure how to go about integrating this function...
Oh, I was unaware of the equivalent form. This makes much more sense now!
One last question though. One of the theorems states that the derivative of an integral is the original function. Does this statement also work in reverse? I.e. the integral of a derivative also yields the original...
Homework Statement
*note that this is the graph of the derivitive of the function f(x).
Homework Equations
Possibly the fundamental theorems of calculus?
The Attempt at a Solution
I know this problem should be easy, but I am not seeing how my book comes to the answer. Below is the...
This implies that after each time I have chosen a letter, there is one less to choose from.
I tried to use n! to find an answer by doing 6x5x4x3x2x1, but the resulting answer was way to large.
Im not sure how this is so easy for you. I assume that the question means that no lettter can be used more than once within one of the 4-letter codes. If this is the case, then there are way to many codes to write by hand.
This problem came from a review worksheet. If this is not a...