What is Rational functions: Definition and 70 Discussions
In mathematics, a rational function is any function that can be defined by a rational fraction, which is an algebraic fraction such that both the numerator and the denominator are polynomials. The coefficients of the polynomials need not be rational numbers; they may be taken in any field K. In this case, one speaks of a rational function and a rational fraction over K. The values of the variables may be taken in any field L containing K. Then the domain of the function is the set of the values of the variables for which the denominator is not zero, and the codomain is L.
The set of rational functions over a field K is a field, the field of fractions of the ring of the polynomial functions over K.
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
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 verticle 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
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...