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    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...
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    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.
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    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?
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    Applying Integration by Parts & Trig Substitution

    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...
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    Integrating a fxn with f(x^2)

    Homework Statement [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...
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    Evaluating point using derivative graph

    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...
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    How many combinations?

    Homework Statement How many 4-letter codes can be formed using the letters A, B, C, D, E, and F? No letter can be used more than once. Homework Equations N/A? The Attempt at a Solution I really didnt know where to begin . . .
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    Simple Trig Limit

    Homework Statement lim x->0 (1-cosx)/sinx Homework Equations (sinx)/(1+cosx) = (1-cosx)/(sinx) sinx/x = 1 The Attempt at a Solution Well, I know I need to change my original limit, as I cannot let the denominator be 0. I usually try to factor out things, but there is nothing to...
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    Domain/Range for Inv. Functions

    Homework Statement Determine if each of the following is true or false. If false, give a counterexample. Arccot (cot x) = x for all x Homework Equations cot= 1/tan x Principal values of tan are -90 degrees <x <90 degrees Capitalization of trig function indicates a function with...
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    Write equation of translated graph in general form

    Homework Statement Identify the graph of each equation. Write the equation of the translated graph for T(-5,6) in general form. Then draw the graph. 4x2 + 5y2 = 20 Homework Equations Ax2 + Bxy + Cy2 + Dx + Ey + F = 0 The Attempt at a Solution I put the equation instandard form and...
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    Evaluating/Solving Logarithmic expressions/equations

    Homework Statement Evaluate the expression "log base 8 of 16" Homework Equations Don't know of any The Attempt at a Solution I dont know where to begin. I have read the textbook chapter on logarithms three times over, and I am now more thoroughly confused than ever. My textbooks...
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    Geometric Sequences & Series

    Homework Statement The sum of the first six terms in a geometric sequence of real numbers is 252. Find the sum of the first four terms when the sum of the first two terms is 12. Homework Equations Sn = A1 - A1Rn divided by 1 - R R \neq 1 (I cant figured out how to make the...