Rational functions — 70 discussions

Homework Statement Hi all. My question has to do with integrating rational functions over the unit circle. My example is taken from here (page 2-3): http://www.maths.mq.edu.au/%7Ewchen/lnicafolder/ica11.pdf We wish to integrate the following \int_0^{2\pi } {\frac{{d\theta }}{{a + \cos...

Hi all This is my first post so please be gentle with me! Limit of this rational function as x approaches infinity? f(x) = (x^3 - 2x)/(2x^2 - 10) I was under the impression that if the degree of the polynomial of the numerator exceed that of the denominator then there could be no...

Homework Statement Find an equation of a rational function f that satisfies the given conditions: vertical asymptotes: x=-3, x=1 horizontal asymptote: y=0 x-intercept: -1; f(0)= -2 hole at x=2Homework Equations The Attempt at a Solution Vertical Asymptotes are (x+3) and (x-1). Also (x-2)...

Hi, I was wondering whether two rational functions f,g whch coincide on the unit circle actually coincide on all of C. I would say yes. Let D be the set of all complex numbers with the poles of both f and g removed (let's assume there are no poles on the unit circle). This is then open...

Homework Statement ∫1/ x^3-1 dx, ok how would i do this Homework Equations ∫dx/ x^2+a^2= 1/a tan^-1 (x/a) +c i tried to simplify x^3-1 = (x+1)(x-1)(x+1)

Homework Statement ∫ 10/(x-1)(x^2+9) would i change this into 10/ (x-1) (x+3) (x+3) then= A/ x-1 + B/ X+3 + C/ x+3

Evaluate the Integral: \int \frac {2x+1}{(x^{2}+9)^{2}} My attempt: \frac {2x+1}{(x^{2}+9)^{2}} = \frac {Ax+B}{x^{2}+9} + \frac {Cx+D}{(x^{2} + 9)^{2}} = (Ax+B)(x^{2} + 9)^{2} + (Cx+D)(x^{2} + 9) = Ax^{5} + Bx^{4} Dx^{3} + (18A + E)x^{2} + (81A+9D+18B)x + 9E + 81B I'm not sure what...

Homework Statement Find asymptotes for f(x) = (x^2 -1) / (x - 1). (if exist) Homework Equations g(x) is a (horizontal or oblique) asymptote if lim |f(x) - g(x)| = 0 (here, lim is to be limit as x goes to infinity. don't know how to type it) or if q(x)/p(x) = g(x) + r(x)/p(x)...

First Question If: f(x) = (x^2+1)/x Then: f(x) = x + (1/x) From my understanding, x would be the oblique/slant asymptote. Why is that? Second Question Why and how can horizontal asymptotes be crossed?

i'm trapped with a problem: \int\frac{dx}{x\sqrt{2-x-x^2}}. i think this problem could be solved by subtitutions: \ x+\frac{1}{2}=\frac{3}{2}sint and \ u=tan\frac{t}{2}. and finally we would get an expression in \ u: \frac{\sqrt{2}}{4} log\left|\frac{2\sqrt{2}+u-3}{2\sqrt{2}-u+3}\right| (am...

Homework Statement Find two constants for 'a' and 'b' such that the vertical asymptote will be \pm \frac{3}{5} y=\frac{ax^2+7}{9-bx^2} I rearranged so that it becomes -bx^2+8 in the denominator since i know that there are two roots that are \pm it must be a square and since 3 is the...

I have trouble with Graphing rational functions, please help me,test is tomorrow I do not know how to use horizontal , vertical , oblique asymptotes to graph a rathional functions. like y=2x+3+3/x+1; y=x^2-4/x-4 thank you very much

http://planetmath.org/encyclopedia/CPlace.html, how do I rewrite (2) to get the third equation R(z)=... ? thank you

4 The height, x metres, of a diver above a swimming pool at time t seconds after he has bounced from the diving board can be modeled by the function x(t)= 3- 3t (3t^2/2) a How long, in seconds, after he has bounced from the diving board does the diver reach his maximum height? b What is the...

Integrals of Rational Functions... The integral of:... (x-1)/x^4+6x^3+9x^2 , dx...i factored out the bottom getting: x^2(x+3)(x+3)...so, my new integral is: (x-1)/x^2(x+3)^2... now when i muiltlpy both sides by (x-1)/x^2(x+3)^2...i get... x-1= A(x+3)^2 + Bx^2(x+3) + C x^2...for A i got...

Suppose 2 cuadratic functions: ax^2+bx+c, dx^2+ex+f. Suppose that the first one is upside with its minimum above the x line reference, and the second one is downside with its maximum above the x reference, and suppose that the two functions intersect at two points that pass through straight line...

How do I solve the integration of a rational function such as: x^2 - 6x - 2 (x^2 + 2)^2 If possible, please list the general rule of solving, I DO NOT want the answer, I simply want to know the way of solving it. Thanks in advance! So far I got to the part where A = 1, B = -6 and...

How do I solve the integration of a rational function such as: x^2 - 6x - 2 (x^2 + 2)^2 If possible, please list the general rule of solving, I DO NOT want the answer, I simply want to know the way of solving it. Thanks in advance!

Can someone pls help me solve this integral? integral of (6x^2-13x-43)dx/(x^3-1x^2-8x+12) it's supposed to be solved using partial fractions, but I am having trouble factoring the denom correctly so I can apply it... Thanks

I've just finished reading the section on partial fraction integration from my text. The book describes how all rational functions can be integrated by performing a partial fraction decomposition and subsequently integrating the partial fractions using methods that are already known. I tried to...