Simplifying Definition and 487 Threads

I was trying a while ago to prove associativity of the XOR operator. That led me to the following problem: I am trying to prove \overline{(\overline{A}*B+\overline{B}*A)}*B + \overline{B}*(\overline{A}*B+\overline{B}*A) = B Obviously it can be solved by just creating a truth table...

Homework Statement I solved my original question so I posted another one. http://i.imgur.com/dpevY.png Find R_{eq} at terminals (c,d) Homework Equations R_{eq} in series = Ʃ R R_{eq} in parallel = \frac{1}{R_{1}} + \frac{1}{R_{2}} + ...+ \frac{1}{R_{n}} The Attempt at a Solution I don't...

P(S1 \cap S2 \cap S3 | r) How do I simplfy the above equation if S2 and S3 are independent of r ?

Homework Statement I've come across the type of sum in several places/problems but seem to be making no progress in trying to simplifying it further. We have a finite series of some exponential function. \sum_{n=0}^{N}e^{-na} Where a is some constant, a quantum of energy or a...

Homework Statement Hello! I'm guessing this is precalculus. There is an intermediate step in a simplifying process and I got to: \sum_{x=1}^n xA^{-Bx} Where A is a constant and B is a constant. Homework Equations I was wondering how to write this without the summation sign...

Homework Statement The original problem is \int \, \frac {xe^{2x}}{(1+2x)^2} dx . I utilized integration by parts to get: -\frac {xe^{2x}}{2(1+2x)} \, + \, \frac {1}{4}e^{2x} \, + \, C which I know is correct. However, I am told by the book that this may also be expressed as...

Hi, I'm trying to work this out. Just a small question: Let (X, m, μ) be a measure-triple (X a set; m a sigma-algebra, μ a measure) , and let, f:X-->ℝ be measurable. For B a Borel set, define : v(B):=μ(f-1(B)). Then show: a)v is a measure in the Borel subsets of R , and...

Homework Statement Find the derivative of arctan[(1 - x) / (1 + x)]. Homework Equations Everything in the "Show Steps" section: http://www.wolframalpha.com/input/?i=derivative+arctan%5B%281+-+x%29+%2F+%281+%2B+x%29%5D My problem is that I don't know how Wolfram manages to simplify...

Homework Statement Find derivative of sin^-1 (2x + 1) Homework Equations I do everything Wolfram does except I don't know how to simplify to get the final answer. http://www.wolframalpha.com/input/?i=derivative+sin%5E-1+%282x+%2B+1%29 The Attempt at a Solution Everything Wolfram...

Homework Statement Find the derivative of: y = 10^(1 - x^2)Homework Equations I get: y' = (10^(1 - x^2))(ln 10)(-2x) doing everything Wolfram does here: http://www.wolframalpha.com/input/?i=derivative+10%5E%281+-+x%5E2%29 I don't understand why it simplifies to Wolfram's final answer from...

Homework Statement Finding the derivative of x^2 sin x tan x. I need to simplify this: x^2 sin x sec^2 x + x^2 tan x cos x + 2x sin x tan x to: x (x sec(x) tan(x) + sin(x) * (x+2 tan(x))) Homework Equations Just what you see above.The Attempt at a Solution I can get it simplified to x(sin...

Homework Statement Reduce the resistor network to a single resistor. Go step-by-step and indicate the series or parallel combinations being reduced. Homework Equations For series resistors: R_T=R_1+R_2+R_3+\cdot \cdot \cdot +R_N For parallel resistors...

I have to simplify (or get it in terms of tan I guess?) \cot (\frac{2\pi }{3} - x) I'm not sure how to get the reference angle and subtract the angle 'x' from it to get an expressional value...how would I do this?

Homework Statement Simplify the following expression: x3(1-x2) / x(x-1) Homework Equations The Attempt at a Solution I know that the top can be factored to x3(1-x)(1+x) to give x3(1-x)(1+x) / x(x-1) . However, after this step I seem to just go round in circles. I got an...

Simplify (x+3)1/2 - (x+3)3/2 i honestly am so lost on this one how i approached it was (x+3)1/2 [1 - ((x+3)3/2 / (x+3)1/2)] but again, i have no idea what I'm doing.

Homework Statement Solve for s: -4su+7t+9u+2=6t+4u-9 Homework Equations The Attempt at a Solution My answer: s = \frac{-t-5u-11}{-4u} The given answer: s=\frac{t+5u+11}{4u} I know that the right hand side has been multiplied by -1, but this raises some questions in my mind; Why...

Homework Statement (n+1)(n+1)!+(n+1)! =(n+2)! simplify The Attempt at a Solution I need to know how to simplify this to show it is true. I know that the above statement is true, but I do not understand how to simplify the left hand side to show it. Thanks, I really have no idea where...

Hi, I have question where I am asked to find the % overshoot of a system based only on its transfer function. T(s) = 15(s+2.1) (s+2)(s2+4s+29)(s2+2s+50) I'm assuming I need to use second order assumptions and then find the damping...

Homework Statement Simplify ln [(e^1-3ln2)/(2∏/e)] Homework Equations I was using the equation e^lnx = x to try and simplify the numerator, but I am unsure if that is correct. The Attempt at a Solution I am very rusty with my calculus and when it comes to using ln, I tend to get stumped...

Homework Statement Simplify. \sqrt[3]{\frac{5}{4}} The answer according to the textbook is: \frac{\sqrt [3]{10}}{2} Homework Equations -- The Attempt at a Solution Separated numerator and deonominator into individual cube roots and multiplied both by \sqrt[3] {4} ...

How would you approach something like this? \sqrt{-\sqrt{3}+\sqrt{4+\sqrt{5}+\sqrt{17-4\sqrt{15}}}}

Homework Statement Simplify...Homework Equations Starting Equation: ³√9xy^4 * ³√12x³yThe Attempt at a Solution (Sorry ahead of time if this is sloppy) ³√9xy^4 * ³√12x³y - I broke up each part of the cubed roots to try and simplify them³√9 * ³√x * ³√y * ³√y³ * ³√y * ³√12 *...

Homework Statement The expression can be simplified. Simplify the following...Homework Equations 1 _____________ - Starting equation √3 + √2 - √5The Attempt at a Solution 1 * [(√3 + √2) + √5] _____________...

Homework Statement Is it possible to simplify this even further? Homework Equations This is a Secant-tangent equation. Secant: AD = 18/radical 3 AC = ?? The Attempt at a Solution I cross multiplied to get 18=324radical 3 (AC) and in the end i got 0 = (18radical3) (AC) which makes...

Homework Statement Hello, I am trying to simplify the inputted function here http://www.wolframalpha.com/input/?i=sqrt%282%29+sqrt%281-cos%28%282pi%28x-y%29%29%2Fn%29%29 which is \sqrt{2}\sqrt{1-cos[2\pi(x-y)/n]} to the form of 2sin[(x-y)\pi/n] Homework Equations Not sure The Attempt at a...

Homework Statement simplify -x^3 - 3x^2 - 4x - 2 It is equal to -(x-1)(x^2 + 2x + 2) Not sure how to get that answer, nor how to start it.

I know the generalized formula for Feynman parameters, my problem is in simplifying. What I mean is something like this: Take the simplest 3 parameter equation \frac{1}{ABC} = 2 \int_0^1 dx \int_0^1 dy \int_0^1 dz \frac{ \delta \left( 1-x-y-z \right)}{(xA+yB+zC)^3} And you can take this...

Homework Statement I'm actually asked to calculate the area under the curve 5x + x2 over the interval [0,1] using Riemann Sums. I found the formula for the Riemann sum over the interval, it being the following: \sum^{n}_{k=1} (\frac{5k}{n}+\frac{k^{2}}{n^{2}})(\frac{1}{n}) However, I...

Homework Statement Simplify (\sqrt{3+4i}+\sqrt{3-4i})^{2} Homework Equations The Attempt at a Solution well I tried expanding it out but I don't think that is the right approach but I have no other idea to tackle the problem? so by expanding I had...

for example if f(x) = \frac{x^{2} - 1}{x+1} they by factoring: f(x) = \frac{x^{2} - 1}{x+1} = \frac{(x + 1)(x - 1)}{x+1} = x - 1 thus the simplified version is x - 1 let's say g(x) = simplified f(x) g(x) = x - 1 meaning g(x) = f(x) but g(-1) ≠ f(-1) am I missing something?

Hello, I need help trying to simplify the equation below, I believe it should be in terms of x and constants only, no trigonometry. "Simplify arctan(cot(x)), assuming 0<x<pi/2" After many attempted solutions and failures, my most recent attempt is below. let arctan(1/tanx) = u ==> tan...

Homework Statement 3b^1/2 x 4b^0 / 6b^1/2 3. The Attempt at a Solution [/b] All the solutions i keep getting do not equal the answer which is 2b^-1 = 2/b. I am not sure what i am supposed to minus from the first side and put on the second side of the equation?

Homework Statement Find a power series for the function, centered at c, and determine the interval of convergence. Homework Equations g(x) = 2 / (1-x^2) , c=0 The Attempt at a Solution 2 / (1+x)(1-x) = 1/(1+x) + 1/(1-x) 1/(1-(-x)) => Sum [(-1)^n (x^n)], n=0 to infinity. Converges when...

I don't know if this is calculus or not but this was on a calculus test. It was the last step of a third derivative question. I lost a mark because the teacher says (x^2-1)/x^2 is more simplified than 1-(1/x^2).. is this fair? Is there an official rule that states (x^2-1)/x^2 is more simplified...

Hi, I am trying to simplify this; x \frac{\partial}{\partial x} W(x,y) - \frac{\partial}{\partial x} (xW(x,y)) Am I correct in thinking I can do this with the product rule, as; \frac{\partial}{\partial x} (xW(x,y)) = \left( \frac{\partial x}{\partial x}\right) W(x,y) + x...

Hi everyone and nice to meet you. I'm velox_xox a newbie to PF and a high school correspondence student currently taking Algebra II. Since I'm correspondence, I am basically teaching myself my subjects, which means if I don't understand something it's a big problem. I enjoy math, but I must...

Homework Statement I'm trying to self-study Mary L. Boas' book Mathematical Methods in the Physical Sciences. One of the exercices asks the reader to find the limit of n -> ∞ (n!)2 / (2n)! Homework Equations None The Attempt at a Solution Instinctively I know that (2n)! grows...

Homework Statement I'm trying to see if what I have before the e match up with the correct answer. the correct answer is (2+.5i)e^(1+3i)x + (2-.5i)e^(1-3i)x The Attempt at a Solution This is what I have so far. I don't know how I would simplify anymore. Please help.

Hello All, I can compute the solution, but I fail to see how it further simplifies into the final expression. The solution manual lists both the answer and its simplified formulation. How do I go from step three to step four? Homework Statement Find the derivative of: f(x) =...

Homework Statement Hello, I'm an audio engineer with an interest in creating/implementing audio processing techniques and I'm trying to learn IIR filter design via the Bilinear Transform method. I've looked through various books and online resources but I keep on getting stuck when it comes...

I have the following limit problem: $$\Large\lim_{x \rightarrow \infty}\frac{x^{\frac{5}{3}}}{e^{2x}}$$ I have reduced it to the following using L'Hôpital's rule once and basic algebra: $$\Large\lim_{x \rightarrow \infty}\frac{5}{2e^{2x}3x^{\frac{-2}{3}}}$$ I can tell that the limit is 0, but...

u is a complex. Can this sum be simplified? If so, how? $\displaystyle \sum_{n}^{\infty}\frac{2u+5}{2}\left(-\frac{u}{2}\right)^n $ Thanks.

Homework Statement I uploaded a picture of the question because I didn't want to confuse people from the way it looks because it is pretty long. http://tinypic.com/r/2itpm39/5 Homework Equations -None- The Attempt at a Solution I went from the original equation and took an 'x'...

I have solved this equation but I am just not quite sure why this final result is the way it is. \frac{2e^{t}+C}{e^{t}} = 2e^{-t} + C Why is it e^{-t} when its simplified ?

Homework Statement Expand and simplify algebraic expressions. Homework Equations (2a+1)(3a-1)(a-2) The Attempt at a Solution The problem is, we normally always do these problems with only two sets of brackets. I tried just multiplying each number will each other number but it...

I am trying to simply G1 = G1(1+F1) / (1 + G1F2(1+F1)) in terms of G1, G2, H2, and H3 where F1 = G2/(1-G2H2) and F2 = G3 / (1-G3H3) i got the result (G1(1-G2H2)(1-G3H3) + G1G2(1-G3H3)) / ((1-G2H2)(1-G3H3) + G1G3(1-G2H2) + G1G2G3) however, the book gives the result with a +1 in the...

Homework Statement It has been a while since I have really been involved in trig seriously, But I felt it appropriate to go in this particular forum because in my classes from years back "precal" was the title associated with trig (: The Problem: sin(X) / sin(X/2)...

When simplifying a circuit, can a parallel branch with a current source and a resistor in series be considered as just the current source? Also, if two parallel current sources 'point upwards' i.e. toward the positive rail, can I add them together as one source even if there are other...

Homework Statement So i think i found the general solutions to both these separable equations, but I am not sure if I am suppose to simplify any further to get it in explicit form, and how i can even do that. Homework Equations The Attempt at a Solution 1. \frac{dy}{dx} -...

Homework Statement Simplify this expression: csc(x)sqrt(sec^2(x)-1) with 0 less than or equal x less than pi/2. Homework Equations The Attempt at a Solution Not really sure what they want here, but would a good place to start be to square the entire expression to get rid of the...