Rational Definition and 616 Threads

(BGR,1989) Prove that for any integer $n>1$ the equation $\displaystyle \frac{x^n}{n!}+\frac{x^{n-1}}{(n-1)!}\cdots+\frac{x^2}{2!}+\frac{x^1}{1!}+1=0$ has no rational roots.

Homework Statement Find the Values of B and C given this: \frac{(3x-18)}{(2x+1)(7x-3)}= \frac{B}{2x+1} + \frac{C}{7x-3} Homework Equations The equation given: \frac{(3x-18)}{(2x+1)(7x-3)}= \frac{B}{2x+1} + \frac{C}{7x-3} The Attempt at a Solution My attempt: \frac{(3x-18)}{(2x+1)(7x-3)}=...

Homework Statement evaluate. Homework Equations lim_{x->0+} \frac{\sqrt{x}}{\sqrt{sinx}} The Attempt at a Solution i've tried l'hopital's and it is just endless cycle.

Homework Statement evaluate the integral. Homework Equations \displaystyle\int {\frac{1}{secx+tanx} dx} The Attempt at a Solution can i just do ln|secx + tanx| ??

Homework Statement evaluate the integral.Homework Equations \displaystyle\int {\frac{3x+2}{\sqrt{1-x^2}} dx}The Attempt at a Solution - i tried factoring hoping for a perfect square that i could take the square root of, but that doesn't work. -u-sub won't work: u=1-x^2 ; du=2x -i don't know...

Homework Statement evaluate the integral. Homework Equations \displaystyle\int_2^∞ {\frac{2}{v^2 -v} dv} The Attempt at a Solution how does this integrate into: 2 ln| \frac{v-1}{v}| i tried and got 2ln|v^2-v| but not above.

When I plot y = 3x^{\frac{4}{3}}-\frac{3}{32}x^{\frac{2}{3}}, I get: https://dl.dropbox.com/u/5653705/pfgraph1.png but I don't see any reason for the domain to be restricted to x > 0 . There is only a cubic root, which is well defined for negative numbers ... I've tried on a few...

Let f(x) be a function which is defined in the open unit disk (|z| < 1) and is analytic there. f(z) maps the unit disk onto itself k times, meaning |f(z)| < 1 for all |z| < 1 and every point in the unit disk has k preimages under f(z). Prove that f(z) must be a rational function. Furthermore...

Homework Statement Homework Equations The Attempt at a Solution Alright so the solution is in the above pic, but I can't get anywhere close. You can see from the green circles that the "squares" aren't matching up. So I'm not sure if I can't multiply fractions anymore or what.

Homework Statement Integrate the following: Homework Equations ∫(x^2+x-7)/(x+3) The Attempt at a Solution The only way I can think of solving this would be to split up each term into a separate fraction.

Homework Statement integrate the following:Homework Equations ∫(x/(x-1)^3The Attempt at a Solution i've tried u-substitution, finding an inverse trig function that matched the formula, and still can't figure out how to solve this problem. u-subtitution for u=x gives the same problem...

rational number to count the next rational number from any rational number? We can count the next natural number, but we can't count the next rational numer.

prove , if x is a rational number , x ≠ 0 then , tan(x) is not rational this theorem was proved by a mathematician called Lambert , I search for the proof , anyone knows it ?!

Homework Statement How may I find stationary points, increase/decrease intervals, concavity for f(x)=(x^3-2x^2+x-2)/(x^2-1)? Homework Equations The Attempt at a Solution I am familiar with how it should be done, except that here I get f'(x)=x^4-4x^2+8x-1 for the numerator of the...

Hi everybody! I've hit a blank with regards to this 1 equation on a old exam paper - think I've overloaded myself a bit and just feel a bit like a airhead at the moment! I understand the actual method and getting to the answer but it starts off with a equation which you then need to get to...

Homework Statement Let p(x,y) be a positive polynomial of degree n ,p(x,y)=0 only at the origin.Is it possible that the quotient p(x,y)/[absolute value(x)+absval(y)]^n will have a positive lower bound in the punctured rectangle [-1,1]x[-1,1]-{(0,0)}? Homework Equations The Attempt at a...

I am reading linear algebra by Georgi Shilov. It is my first encounter with linear algebra. After defining what a field is and what isomorphism means he says that it follows that every field has a subset isomorphic to rational numbers. I don't see the connection.

I think the technique that is to be used for these types of problems, but I just am having trouble grasping why it is permitted. I have no problem with any homework, but it just doesn't seem right. Maybe my text is just not being clear (Larson, 9th, btw) Given a function...

Some bits are ok but I thought I would include them anyway as it is needed to answer the other parts of the question. I have labelled the parts which I need help with. (a) Recall why there are no integer solutions \(m, n \in \mathbb{N}\) to the equation \(m^2 = 2n^2\). ANSWER = an irrational...

Real Analysis--Prove Continuous at each irrational and discontinuous at each rational The question is, Let {q1, q2...qn} be an enumeration of the rational numbers. Consider the function f(x)=Summation(1/n^2). Prove that f is continuous at each rational and discontinuous at each irrational...

For the years 1998-2009, the number of applicants to US medical schools can be closely approximated by: A(t)= -6.7615t4+114.87t3-240.1t3-2129t2+40,966 where t is the number of years since 1998. a) graph the number of applicants on 0<= t <= 11 b) based on the graph in part a, during what...

Homework Statement http://tinypic.com/r/14uet5i/6 just in case it didnt work http://tinypic.com/r/14uet5i/6 how do i find the equation of those two graphs? Also Homework Equations The Attempt at a Solution 1. asym is at -2 so bottom must have (x+2) what's the...

Homework Statement Let \theta \in [0,1] and n \in \mathbb{Z} . Let n\theta mod(1) denote n\theta minus the integer part. Show n \theta mod(1) is a discrete subset of [0,1] if and only if theta is rational.The Attempt at a Solution I'm having a bit of trouble with the "only if" part...

Solve the rational inequality (a-5)/(a+2) < -1.This is what I got so far: a-5/a+2 = -1 a-5= -a-2 0= -2a+3 subtract 3 from both sides: -3=-2a Divide by -2 3/2=a I know that the answer is (-2, 3/2), but I'm not sure where the -2 in the answer comes from. Thanks!

(3/x-2) - (4/x+2) / (7/x2-4) I got it down to... -x+14/7 but the book is showing x-14/7

Homework Statement I need to compute \int_0^\infty \frac{dx}{x^3+a^3}.Homework Equations If f = g/h, then Res(f, a) = \frac{g(a)}{h'(a)}. The Attempt at a Solution In the first I've used a semicircular contour in the upper plane that is semi-circular around the pole at -a. So I calculate the...

My final answer matches that of the textbook, but do I need to change the < to > at any point as I solve this? I ask because, if I assume x is 1 (until I solve for x), then the question statement and parts of the solution are made untrue. Homework Statement Solve the following for x...

The function is f(x) = 2x / x3 - 6x2 + 3x + 10 I was taught that any rational function with a numerator of smaller degree than the denominator has a horizontal asymptote at y = 0, which would apply in this case. This makes sense for the end behaviors because as x approaches +/- ∞, y...

I just got this assignment for math and the question was is it possible to have a cubic asymptote in a rational function. If so explain how and where.

how to find the range of rational functions like f(x) = \frac{1}{{x}^{2}-4} algebraically , i graphed it and seen that (-1/4,0] can not be in range . generally i am interested in how to find the range of functions and rational functions in particular

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...

I have a theory that i need to prove but I am not quite sure how to mathematically prove that it is true. Theory: When you square a rational number, each of the prime factors has an even exponent. For example, 10 --> If i square 10, which is a rational number, =10^2 =(5^2 x 2^2)...

Ok all save y'all a little reading. Worked out the problem. Got X^2+2x-1=A(2x-1)(x+2)+bx(x+2)+cx(2x-1) Ok then you write it standard form for a polynomial. Then use can use there coefficients to write new equations at you get 2a+b+c=1 3a+2b-c=2 and finally -2a=1 Now you solve for...

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 x^3-8x+10=0 Homework Equations The Attempt at a Solution By dividing by x-1 (1 is a factor of the solution), I got (x-1)(x2+x-7)+3+10=0 which equals x^3-8x+20=0 I think the solution would be imaginary but I used a graphing calculator and there is one...

Homework Statement "Prove m√n is not a rational number for any natural numbers with n,m > 1, where n is not an mth power" Homework Equations Natural numbers for us start at 1. Since we know n is not an mth power, then n \neq km for an arbitrary integer k. The Attempt at a Solution...

On a math test, one of the questions was to solve -\sqrt{7-x}=-\frac{x^2}{2}+12x-10. I solved graphically with a calculator, but later tried to solve algebraically, when I had more time. The equation is equivalent (with extraneous solutions) to x^4 + 48x^3 +536x^2 -956x + 372=0. This quartic has...

Show that there are infinitely many rational numbers between two different irrational numbers and vice versa. So I started as such: WLOG let $a,b$ be irrational numbers such that $a<b$. By theorem (not sure if there is a name for it), we know that there exist a rational number $x$ such that...

I am given the number $.334444\ldots$ So we have $0+33\times 10^{-2} + \sum\limits_{n=3}^{\infty}4\times 10^{-n}$ Is there a way to put this all together in one geometric series?

Hello, I have a simple question that has bothered me forever.When I am given a rational function, say, f(x) = (x2+x-6)/(x+3)say I want to look at the domain of this function. Well the first thing that catches my eye is the fact that if I plug in x=-3, the denominator will be 0, which would be...

Homework Statement If r is a rational function, use Exercise 57 to show that ##\mathop {\lim }\limits_{x \to a} \space r(x) = r(a)## for every number a in the domain of r. Exercise 57 in this book is: if p is a polynomial, show that ##\mathop {\lim }\limits_{x \to a} \space p(x) = p(a)##...

can someone help me (4a 3/2)(2a1\2) (3x5/6)(8x2/3) (27a6)-2/3 the fractions are powers

Homework Statement To find the oblique asymptotes of a rational function (i) f(x)=\frac{P(x)}{Q(x)}=\frac{a_{n}x^{n}+a_{n-1}x^{n-1}+...+a_{0}x^{0}}{b_{m}x^{m}+b_{m-1}x^{m-1}+...+b_{0}x^{0}} where n=m+1 we exprese it in a form (ii) f(x)=ax+b+\frac{R(x)}{Q(x)} using long division (my book...

Homework Statement Find the inverse of a rational function: f(x)=\frac{2x}{x-2} The Attempt at a Solution 1. Verify the function is one-to-one. Question: is there a way to do that withought drawing the graph? Some algebraic method? I know that this means that the function crosess any given...

Homework Statement Show that Q does not fulfill the completeness axiom. Homework Equations "Every non empty set of rational numbers that contains an upper bound contains a least upper bound" (show this is false) The Attempt at a Solution I've sat on this question for a few days...

Homework Statement <Indefinite integral sign here>[r^2 -2r] / [r^3 - 3r^2 + 1]dr or the second example in the "Substitution" section here: http://people.clarkson.edu/~sfulton/ma132/parfrac.pdf Homework Equations nada. The Attempt at a Solution Nothing to really attempt, I just...

Homework Statement u^2 --------------- u^2 - 4 Homework Equations I am told that this is equal to 1+ 4/u^2 - 4The Attempt at a Solution No clue how these two are related. Factor out a u^2/u^2? But that alters the denominator. My next that is partial fraction decomp. Am...

EDIT: Problem found. This thread can now be ignored.Homework Statement Find the indefinite integral. Homework Equations ((y^2-1)/y)^2 dy The Attempt at a Solution I've attempted a few things. I first attempted to split the statement inside the outer parentheses into two fractions; (y^2/y...

Homework Statement I am trying to find when the square root of the expression 25+8a^2 is rational, where the number a also needs to be rational. \sqrt{25+8a^2}=b, where a and b are both rational numbers. I am trying to get an expression for a in terms of some other number m, which would always...

Homework Statement Find the inflection points and use second derivative test to determine where the function is concave up or down Homework Equations f(x) = (x - 1)/(x2 - 4) The Attempt at a Solution f'(x) = (-x2 + 2x - 4) / (x2 - 4)2 f''(x) = 2x3 - 6x2 +24x -8 / (x2-4)4...