Polynomial Definition and 1000 Threads

Homework Statement http://img213.imageshack.us/img213/7867/problemeigen.png Uploaded with ImageShack.us Homework Equations http://img339.imageshack.us/img339/771/equationh.jpg Uploaded with ImageShack.usThe Attempt at a Solution so i tried doing the problem i going to use L for lambda i...

Homework Statement f:[1,+∞[→ℝ x→sqrt(x+2)-sqrt(x-1)Homework Equations show that f([1,+∞[)=]0,sqrt(3)]The Attempt at a Solution Any tips on how to start it.

Homework Statement f:]1,+∞[→]2,+∞[ x→ 2x/(x-1) Homework Equations Prove that f is injective and serjective. The Attempt at a Solution I already proved that it's injective by stating the injectivity law: for every (a,b)ε]1,+∞[: f(a)=f(b) implies a=b so: 2a/(a-1)=2b/(b-1)...

Is there a good way to do this? I have an equation, say x^3 - 4*x^2 + 2, so a=1, b=-4, c=0, d=2. Is there an easy way to express the largest root of such an equation? In this case, the roots are: 3.8661982625090223 -0.65544238154983 0.7892441190408067 But I am trying to find an...

Homework Statement What is the minimal degree Taylor polynomial about x=0 that you need to calculate sin(1) to 3 decimal places? 6 decimal places? Homework Equations R_nx = f^(n+1)(c)(x-a)^(n+1)/(n+1)(factorial) The Attempt at a Solution I have attached my attempt. I am stuck on the...

I am currently working on a gamma ray spectroscopy lab in which i have just fit a polynomial to my calibration points. The calibration points are in a relatively straight line, from x=40 to x=450, and y=34 to y=1300 for the first and last end points respectively. Where X is channel number, and Y...

I am trying to get MATLAB to be able to produce a symbolic polynomial and am having some issues. The polynomial I would like it to produce is given a d and k, X(k+1)-X(k-d)-X(k-d-1)-...-1 What I have so far is k = 5; d = 3; syms X; i = 0; while (k-(d+i) >= 0) terms(i+1) =...

If you have a polynomial like (1+x)^6 = x^6+6 x^5+15 x^4+20 x^3+15 x^2+6 x+1, What function would you use to pick only the last N terms? For instance, for N=3 pick x^6+6 x^5+15 x^4 I've being using sum of a binomial times something, but was wondering if there is anything more simple. Thanks!

Hi friends, I have been trying to solve the ode of second degree below with respect to z: d2y/dz2=(i/a*z+b)*y i is the complex i, a and b are constants i ended up with the summation of bessel functions of first end second kind. Then I checked with MATLAB ode solver it gives no...

Homework Statement Let T: P2-P3 be the linear transformation defined by T(p(x)) = xp(x). Which of the following are in R(T)? (a) x2 (b) 0 (c) 1 + x Homework Equations R(T) is the the set of all vectors in P3 which are images under T of vectors in P2. The Attempt at a Solution...

Homework Statement Find all zeros of k(x) = 4x^4-7x^2+3x Homework Equations n/a The Attempt at a Solution I don't know if I should find the factors of 0 and 4.. Can you help me what to start out with.. I can do other ones like p(x) = 3x^3-37x^2+84x-24. But this problem k(x) =...

I need help from someone with a graphing calculator. My little brother lost my graphing calculator and synthetic division I can't make work becasue the terms aren't exactly friendly. The equation is, 24.059025x^4 + 94.98287069x^3 + 44.56696001x^2 - 827.1103204x = -1067.832496 The more...

Homework Statement Hi every body I am triyng to find a polynolial approximation to the function: f(x)= (x+2)ln(x+2) using the chebyshev polynomials, the idea is to use MATLAB to find the coeefficients of the approximation poly. using the comand double(int(...)) but this command...

Homework Statement Find the polynomial p(x) of degree 20 satisfying: p(-10) =p(-9) = p(-8) = ...=p(-1) = 0 p(0) = 1 p(1) = p(2) = p(3) = ...p(10) = 0 Homework Equations L(x) := \sum_{j=0}^{k} y_j \ell_j(x) The Attempt at a Solution i tried using the formula above: a =...

Homework Statement Given 2 + 3i is one root of the equation: x^4 - 6x^3 + 26x^2 -46x +65 = 0 Find the remaining roots. The attempt at a solution I am thinking about this as a possible solution although it is too long to be plausible, unless I'm wrong. let x = a + bi and then replace in the...

For any characteristic polynomial determined from A - eI (where A is a nxn matrix, e is an eigenvalue and I is the identity matrix), is it a rule that the coefficient associated with the char. polynomail term of highest degree must be positive ? My tutor made a theory that if the...

Homework Statement A quartic function has x-intercepts of -5, -1, 2, and 4. The point (3.-8) lies on the curve. Determine an equation of the function. Homework Equations The Attempt at a Solution y = k (x+5)(x+1)(x-2)(x-4) Expanded form: f(x)=kx^4 + 9x^2 - 38x + 40 <---My...

Homework Statement 4x5-16x4+9x3+23x2-15x-9 > 0 Homework Equations Synthetic division PQ Rule? The Attempt at a Solution Don't know how or where to begin

Homework Statement Let z^n + \sum_{k=0}^{n-1}a_kz^k be a polynomial with real coefficients a_k\in[0,1]. If z_0 is a root, prove that Re(z_0) < 0 or |z_0| < \frac{1+\sqrt{5}}{2}. Homework Equations The Attempt at a Solution I have attempted to solve this problem by...

Homework Statement Determining the chromatic polynomial Pk(G) for following graph Homework Equations The Attempt at a Solution I did the solution in the picture so i get k and k-1 the colors should not be same as adjacent so that sounds like 2 colors is that all i need to...

Homework Statement 2 People build a sandcastle of 36cm by 48cm by 60cm. Later they learn that the box will be smaller; a certain amount will be taken off each of the length width and height Homework Equations The Attempt at a Solution a) write a p(x) > (36-x) (48-x) (60-x)...

Hello, I'm new here, nice to meet you guys i was in class today and just didn't understand the taylor polynomial approximation, the professor started out approximating a function by polynomials of degree N, he first showed us how a linear polynomial was a crude approximation of the function...

Homework Statement Kaylas lemonade stand has experienced rises /falls in sales caused by temperature changes over 2 summers. Her sales over the first two weeks of summer were tracked according to the model S(x) = x^3 -12x^2 +36x, where x is the number of days and S(x) is the number of sales...

Ive attached the problem and my work in the pic. Questions: Am I even applying the taylor polynomial the correct way? (I never learned taylor series, but I was supposed to be taught in the pre-requisite class) Am I suppose to plug in c=4? I am not so sure about how the U4(t) works...

Homework Statement Why is this not a polynomial function? h(x) = 3x + 2x Homework Equations The Attempt at a Solution 3x+2x = 5x. 5x is a linear function with a degree of 1, why is this not a polynomial funct?

Homework Statement Determien an euation for each polynomial function described below state whether the function is even, odd or neither. Sketch a graph of each. Homework Equations The Attempt at a Solution My question is.. If youre given information like this :: a) A quintic...

Homework Statement What is the difference between f(x)= x^3 , and g(x) = x^3 - x What does that -x do to the function and how do you represent it graphically? What about f(x) = 3x^3 +x Homework Equations The Attempt at a Solution No idea, wolframalphad the graph but i...

Homework Statement We know that a polynomial function is anything with a positive exponent and a rational number. a) - / x^3 -4 d) 3x^-1 - 11 g) y= [sqrt of term]3x^2 -5x Homework Equations The Attempt at a Solution c) 1 / x^3 - 4 (do we use exponents to verify ?)...

Homework Statement Given p(x) = x4+2x2+1 and A = [[1 1 -2 0] [0 1 0 2] [1 1 -1 1] [0 0 -2 -1]] p(A) = 0 Find a polynomial q(x) so that q(A) = A-1 a) What is q(x)? b) Compute q(A) = A-1 Homework Equations I found the Cayley-Hamilton theorem, which states: p(x) = det(A-xIn)...

As it turns out, this first part was an extremely pervasive user error that I have not seen for days. Still, though, it is interesting that equations can be factored in many different ways, so I will post that here instead: 3x^3 = -5x^2 +2x -3x^3 -5x^2 + 2x = 0 Factored: x(-3x+1)(x+2) and...

Homework Statement Examining the answers of the previous two questions, write the quadratic polynomial f(x1,x2,x3)=x1x2−6x22+3x2x3−3x23 in the form f(x1,x2,x3)=[x1x2x3]A[x1x2x3]<-this last group is a column matrix where A is a symmetric matrix. Homework Equations Matrix multiplication...

Homework Statement (There is a comparison question I have, so i'll post my question with these) 8) Each of the following polonomials has x-intercepts of -6, 5 , and 0. Determien the appropriate equation for each. Then, sketch a graph of the function. b) A quartic function that extends...

To compute the checksum for some frame with m bits, corresponding to the polynomial M(x), the frame must be longer than the generator polynomial. Why...?

Homework Statement Suppose R is an integral domain and I is a principal ideal in R[x], and I \neq {0} a) Show I = <g(x)> for some g(x)\inR[x] that has minimal degree among all non-zero polynomials in I. b) Is it necessarily true that I = <g(x)> for every g(x)\inR[x] that has minimal...

Homework Statement Prove that 0.493948<\int_0^{1/2} \frac{1}{1+x^4} dx<0.493958Homework Equations This chapter is about Taylor Polynomials, and specifically this section deals with Taylor's formula with remainder: f(x)=\sum_{k=0}^n \frac{f^{(k)}(a)}{k!} (x-a)^k + E_n(x) The general formula for...

Two particles move along the x-axis. Particle one has the position x = 8t^2 + 7t + 2 Particle two has the acceleration a = -8t, and when t=0 v=23. When the velocity of the particles match what is their velocity? I thought of approaching this problem by changing both equations into the...

Homework Statement Give a formula for the extended function that is continuous at the indicated point. (x3-4x2-11x+30)/(x2-4), x=2 Homework Equations The Attempt at a Solution I know that I have to factor the top and bottom so that I can cancel terms that cause the function to...

Hi, I'm trying to learn Fourier transforms by myself. I'm a bit confused about how the trignometric polynomial complex form was derived. I'm referring to this: http://en.wikipedia.org/wiki/Trigonometric_polynomial Now, I haven't taken complex analysis so I only know the basics. I used Euler's...

I want to write an algorithm that gives as output the numbers a_n,\ldots, a_1,a_0, when a matrix A\in\mathbb{R}^{n\times n} is given as input, such that \det (A - \lambda) = a_n\lambda^n + \cdots + a_1\lambda + a_0,\quad\quad\forall\lambda\in\mathbb{C} If n=2, a_2 = 1,\quad a_1 =...

\frac{r^3+3r^2+4r-8}{r-1} how do i solve that? and is there a general formula? thanks! Edit by bored Borek: LaTeX corrected.

Homework Statement A n × n-matrix A satisfies the equation A2 = A. (a) List all possible characteristic polynomials of A. (b) Show that A is similar to a diagonal matrix Homework Equations The Attempt at a Solution A2 = A so, A2 - A = 0 A(A-I) = 0 Our minimal polynomial is x2 - x = m(x)...

Hi guys, Thanks for taking the time to read the post. I have a question related to curve fitting and polynomials that i was hoping someone might be able to help me with. I have a set of x and y data points, all on a graph. I have then calculated the 4th order least squares polynomial...

Today I read about the AKS - Primality test in which the simple theorem For gcd(a, n) = 1, we have (X - a)^n\equiv X^n - a\ (mod\ n)if and only if n is prime. was proven. The if direction is quite trivial from the fact that \binom{p}{k}\equiv 0\ (mod\ p) for 1\leq k < p. The other direction...

Homework Statement f(x,y) = ln(3y-8x) Derive the first and second order Taylor polynomial approx, L(x,t) and Q(x,t), for T(x,T) about the point (1,1) Homework Equations -None- The Attempt at a Solution I do not understand what the question wants, nor do i want a solution. I...

[b]1. Homework Statement The swinging period T(θ) for a small amplitude simple pendulum, is given by T, a constant for a constant length pendulum. If the initial angle θ is large, then the amplitude becomes large and the period needs to be corrected. The correction to the large amplitude...

Homework Statement Suppose that you are given a set of observations (tk,yk), k = 1,...,M. You plot these points on a sheet & it seems that the relationship between (t,y) could be approximated with a second order polynomial. a) Write down the model in the form y = Ax + c. Specify the vectors...

Homework Statement Find the minimal polynomial of a=y^3 in F=Kron(Z/2Z, x^4+x+1). (Calculate the powers of a^2, a^3, and a^4.) Homework Equations The Attempt at a Solution I attempted this trying to follow a similar worked problem in my book: a=y^3 & y^4=y+1 Multiply by...

Homework Statement Divide A(x)= [x3+2x2+3 -4x3-x2-5] [3x2-2 x3-2x2+x+4] by B(x) = [x+4 -3] [-x+6 x+2] on both the right side and the left side. Homework Equations The Attempt at a Solution I am...

Why must a polynomial be finite in length? Is there such thing as a recursive polynomial? Thanks guys!

Please Help me out with this one. Can all patterns in 2D or 3D, have an equivalent equation in polynomial?