Simplifying Definition and 487 Threads

Please refer to the attached image. Is there a way to simplify this question? It looks really messy but I have a feeling there is some nifty way around it. Surely they don't want us to integrate that entire function. I also have no idea about part d) how can some values of lambda result in X...

so I was reading my textbook and was showing steps on applying the quotient rule to the function: y=ex/(1+x2) it went from (1+x2)(ex)-(ex)(2x)/(1+x2)2 to ex(1-x)2/(1+x2)2 I understand the first step, but don't get how they got to ex(1-x)2 in the numerator. can someone please explain the...

hi, I am new in basic electronics course. i m having some problem with simplifying the circuits using boolean algebra. can you suggest me any good book to practice this? and i also need a short chart of the laws.

Hello, Is there some way to express the following integral in terms of some simpler functions? f(x,s) = \int^{\infty}_{-\infty} dk\, e^{-ks} \text{Ai}(-k) \text{Ai}(x-k) where the parameter s \in (0,1) and the coordinate x \in (-\infty,+\infty) The best I can come up with is to...

Homework Statement Simplify, if possible. (6w2-w-3) + (7w2-4w+5) Homework Equations The Attempt at a Solution I attempted to factor both expressions, but they don't seem to be factorable. Is this already simplified as much as possible, or am I missing something?

$\displaystyle\frac{-9b^2(a+3b)^{m+2}(2b-4c)^{2+m}}{4(3a+9b)^{2m+2}(b^2-2b^2)^{2-m}}$ my answer to this is $\displaystyle-\left[\frac{2(b-2c)^2b}{9(a+3b)}\right]^m$ i used some factorization of some quantity to arrive to this answer. but I'm not sure how did that technique works. for...

Homework Statement Simplify: [(sec x)(sec2 x) - (tan x - 1)(sec x tan x)] / sec2 x Homework Equations none The Attempt at a Solution [(sec x)(sec2 x) - (tan x - 1)(sec x tan x)] / sec2 x [(sec x)(sec2 x) - tan x (1 -1) sec x ] / sec2 x [(sec x)(sec2 x) - 0 ] /...

This isn't about any specific problem, I'm just hoping for a bit of advice. I've been out of education for a long time and am now doing an OU degree. I've passed the first level with high marks but have been struggling in some of the maths. Basically, I've been doing calculus and the bit I'm...

Hello, I'm trying to solve this equation. (4-4cos(∏*0.16*4)) - (4-4cos(∏*0.16*3)) It seems like it should be so easy. First I start with the left hand side (∏*0.16*4). Then I take the cosine of that, and then multiply it by 4. Then I do 4 - [answer] to get a value for the full left side...

Homework Statement If ##\displaystyle \tan\left(\frac{\pi}{4}+\frac{y}{2}\right)=\tan^3\left( \frac{\pi}{4}+\frac {x}{2} \right)##, prove that $$\frac{\sin y}{\sin x}=\frac{3+\sin^2 x}{1+3\sin^2x}$$Homework Equations The Attempt at a Solution...

Homework Statement Let ## n \geq 2## be a fixed integer. ##f(x)## be a bounded function defined in ##f:(0,a) \rightarrow R## satisfying f(x)=\frac{1}{n^2}\sum_{r=0}^{(n-1)a} f\left(\frac{x+r}{n}\right) then ##f(x)## = a)-f(x) b)2f(x) c)f(2x) d)nf(x) Homework Equations The...

Without the use of a calculator, and showing your work, simplify: $$\frac{1}{2}\left(\left(239+169\sqrt{2}\right)^{ \frac{1}{7}}-\left(29\sqrt{2}-41\right)^{ \frac{1}{5}}\right)$$ edit: My apologies...I was careless in my first statement of the problem...(Nod)

Heather Jean's of Facebook writes: Simplify, \[-(6y-\gamma)-5(-\gamma+6y)\]

My basic math is failing me again :( My attempt to simply: My teacher's attempt: Ignore the difference in notation. He writes || which signifies (A x B) / (A + B) = A || B And yes I'm aware there is more to simplify but I fail to follow him on the first step

Homework Statement \frac{dq}{dT}=\sum_{i} g_i \frac{dq}{dT} e^{-\frac{ε_i}{kT}} = \frac{1}{kT^2}\sum_{i} g_i ε_i e^{-\frac{ε_i}{kT}} = \frac{1}{kT^2} \bar{ε} q Homework Equations q=\sum_{i} e^{-\frac{ε_i}{kT}} or for degenerate states, q=\sum_{I} g_i e^{-\frac{ε_I}{kT}} The Attempt at a...

I have the following two equations C, L, and R are all constants. I need to somehow get the above two equations and get it to look like this: But I can't get mine to look that nice. I have V1(s) = V2(s)(1+sCR) and I substituded it into equation 1 and it ends up looking messy...

The following was written down as a solution to a problem, \begin{eqnarray} P(\alpha_n) & = & \frac{1}{25} \left[ 9| \langle \phi_n \mid \psi_1 \rangle |^2 + 16 | \langle \phi_n \mid \psi_2 \rangle |^2 + 12 i \langle \phi_n \mid \psi_1 \rangle \langle \phi_n \mid \psi_2 \rangle^* - 12 i...

Can someone please show me how to simplify this expression? I have no clue of how it's done so any help would be appreciated. Thank you! x'y'+xz'+yz+x'yz'+xy'z

Simplify $$\frac{x^2-4x+3+(x+1)\sqrt{x^2-9}}{x^2+4x+3+(x-1)\sqrt{x^2-9}}$$ where $$x>3$$.

Homework Statement Simplify this: y = ((k^1/2)/(l^1/4))/((l^1/5)/((k^1/8)) Ideally I would like to make rather than (k/l)/(l/k) simply (k/l) Homework Equations y = ((k^1/2)/(l^1/4))/((l^1/5)/((k^1/8)) The Attempt at a Solution y = (k^3/8)/(l^1/20)

This equality is given in an example, in my textbook: \int\frac{1}{a^2+x^2}dx=\frac{1}{a^2}\int\frac{1}{1+(\frac{x}{a})^2}dx So, my question is simply... how? This is really more of an algebra question, but it'd really help me to see some more detail here.

Homework Statement -\frac{1}{2}[cos(\frac{\pi+\pi n}{\pi+\pi n}) + cos(\frac{\pi-\pi n}{\pi-\pi n})] Homework Equations cos(u)cos(v) = \frac{1}{2} cos(u+v)+cos(u-v) The Attempt at a Solution I am attempting to use the above trig function to simplify the first function, but I can't seem to...

So I'm to calculate the current intensities in the places I put the ammeters in (yeah, I reckon one of them is turned around :)): http://i.stack.imgur.com/PAmmD.jpg And while I can calculate such things for series or parallel circuits, I was taught I should first try to simplify the...

Homework Statement (2x+3x)/6x = 2-x+3-x I've tried moving the 6 above, splitting it up and so... but i can't figure how to do it. It must be pretty simple, but I am just not seeing it. all helps appreciated!

Homework Statement I have developed an equations for calculating some pollutant concentration as a function of x and y. I'm trying to simplify the problem so that I can write the equation for wp as a function of x. All variables except x and wp are known. Homework Equations...

Homework Statement Find values for x, and y in the following statement: [SIZE="2"]2x-y+\sqrt{4x-y}=x-2y+3+\sqrt{x+5} The Attempt at a Solution I've managed to rearrange the equation, but I cannot eliminate or equate the square roots on the LHS: [SIZE="2"]\sqrt{4x-y}-\sqrt{x+5}=-x-y+3

Homework Statement Simplify; expressing with positive indices. \frac{x^{-2} - y^{-2}}{x^{-1} - y^{-1}} The Attempt at a Solution Hello, I'm doing first year uni math and over the holidays, I forgotten my index laws and as a result I'm stuck on this question :rolleyes: I know that...

So, I was following the derivation in my physics book of: x(t) = c_1e^-(\frac{\gamma t}{2})\cos(\omega_d t)+c_2e^-(\frac{\gamma t}{2})\sin(\omega_d t) Until they simply get to this in one step: Ae^-(\frac{\gamma t}{2})\cos(\omega_d t + \phi) I've tried reading many other sources for this...

Could someone explain how I'd simplify (x2-2x+1)/(x-1) to become x-1? Thanks a bunch!

[SOLVED] Simplifying Expressions Hello all I am a bit confused about the laws I am learning about right now and attempted some of my own exercises to understand them a bit. I have the problem NOT(a < 20 AND (b < 10 OR b > 10)) and I need to simplify it. From my understanding I can use...

Edit: Nevermind, figured it out. Thank you for readingOriginal problem: Find the interval of convergence \sum∞n=1 xn / n * √(n) * 3n Ratio Test, right? an+1/a I get to here and I can't figure out how to get rid of the ns: lim n→∞ abs(x/3)* [n*√(n) / (n+1)*√(n+1)] Solution, They break apart...

I have this problem to simplify with positive exponents: \[\left[(-4a^{-4}b^{-5})^{-3}\right]^4\] So, working with the interior brackets, I applied -3 to the equation, which resulted in: \[-(-64)x^{12}b^{15}\] **because "-4" was not in brackets, the exponent was applied to the 4 only...

Hello, Ive was reading my literature today and it showed me some algebra, which i did not understand how it went from one step to the next... What was done to simplify V= x^2 ( 75-x^2 / 2x ) into V= x/2 ( 75-x^2 ) & then what was done to simplify ^^^ V= x/2 ( 75-x^2 )...

Simplify 8p-3 x (4p2)-2/p-5. This is what I got: First thing I did was flip everything to get rid of the negative exponents: p5/8p3x(4p2)2 next thing I did was multiply the 4p2 by 2 p5/ 8p3x16p4Then I subtracted thep5 from the 8p3 p2/8x16p4 and ended up with 1/128p2 I know that the...

Homework Statement I am looking at an example from my book and I have no clue how this is done.Homework Equations I solved the left hand side and got this 125t3+75t2+50t+4 How did they reduce it to 65t+5?The Attempt at a Solution http://i48.tinypic.com/2v2gpap.jpg

Homework Statement Simplify the following expression: \sum_{ \alpha_1 + \cdots + \alpha_n = k} e^{i(\alpha_1 \theta_1 + \cdots + \alpha_n \theta_n)} Homework Equations \alpha_n = k - \sum_{j=1}^{n-1} \alpha_j 0 = \sum_{j=1}^{n} \theta_j The Attempt at a Solution I am trying to simplify...

Simplifying "Complex" Resistor Circuits Homework Statement Question 1: I have an E&M test coming up and I'm having trouble simplifying complex circuits. Our teacher told us something about "pinching" the wires which I didn't really understand. I found the following link...

Okay so, I am having trouble figuring out what exactly to do in implicit differentiation and usage of the chain rule. Like, I keep getting the wrong answer somehow. See, from what I understand you have to find the derivative of both sides then use the chain rule or something and then solve for...

Homework Statement Simplify. a) \sqrt{x^6} b) 8 \sqrt{x^7y^{10}} - 10 \sqrt{x^7y^{10}} For b, it's y^10. I can't make it look right for some reason. Mod note: Fixed the exponent.[/color] Homework Equations The Attempt at a Solution I can simplify all of them but I don't know when or where I...

Homework Statement I have stumbled upon the following equation on wikipedia http://upload.wikimedia.org/math/b/8/d/b8de8bfcdf40f1793e7b72755161d61f.png To clarify, I am not sure how to simplify the equation of the form x^2/(1-x) = 1/(x^2 - x^-2) as demonstrated in the second line of...

Homework Statement See attached image. Homework Equations The Attempt at a Solution I cannot find any resistors in parallel or series in the circuit. I am confused by the lone branch going from the 10kOhm resistor back to the other end of the same resistor. How do I deal with...

I have attached the problem and my working. It would be much appreciated if someone could check through my working and let me know if I have slipped up anywhere. Thanks in advance Steve

Homework Statement \frac{x^2}{(x^2 -1)} Homework Equations N/A The Attempt at a Solution I know the solution is supposed to be 1+\frac{1}{2(x-1)}-\frac{1}{2(x+1)} and when I did long division, I got 1+\frac{1}{(x^2-1)} , so I'm making progress, but I'm not quite there. What should...

Was just double checking if we can simplify this in the following way, ∫ sinx * √(1 + cos2x) dx = ∫ sinx * (1 + cosx) dx

Homework Statement In a lab we conducted in class we graphed angular acceleration vs torque, and found a positive linear correlation-easy enough. However I am getting rather stuck in simplifying the units of slope in terms of Kg, m, and s... I am fairly sure this will give me that angular...

In a lab we conducted in class we graphed angular acceleration vs torque, and found a positive linear correlation-easy enough. However I am getting rather stuck in simplifying the units of slope in terms of Kg, m, and s... I am fairly sure this will give me that angular acceleration equals...

Homework Statement Simplify the expression completely 3(y)(1/3)-3x(y)(-2/3)(2x) / [(y)(1/3)]2 The Attempt at a Solution My attempt is totally wrong. I can't quit figure out what to do or where to start 3(y)(1/3)-3x(y)(-2/3)(2x) / [(y)(1/3)]2 3(y)(1/3)-6x(y)(-2/3) / y(2/3)...

Homework Statement Simplify the following Boolean expressions to a minimum number of literals (a+b+c')(a'b'+c) 2. The attempt at a solution Whenever I tried this I made no progress in reducing the number of literals, I just reordered the expression. (a+b+c')(a'b'+c)...

Simplify the following expression. (2+1×2)−4×6 =(2+2)−4×6 =4−4×6 =4−24 =−20 My answer was 20 and it was wrong. When i look at this i see, 2 plus 1 times 2 minus 4 times 6 The part I am getting wrong is the minus, which in this case means a -4 instead of a 4. I don't understand how you can you...

Homework Statement I need to show that the lim n->inf ( [(1/n) * sum from k=1 to n of ln(k) ] - ln(n) ) is equal to the lim n->inf ( (1/n) sum from k=1 to n of ln(k/n) ) The Attempt at a Solution I showed that the sum of ln(n) from k=1 to n is ln(n!) using ln(a) + ln(b) = ln(a+b). I...