Fractions Definition and 604 Threads

Hello :smile: I've been stuck on this question for almost 3 hours now, and I still have no idea what to do. We haven't done a question like this in class, although we have done integration with partial fractions. Homework Statement Evaluate...

Homework Statement \int^{1}_{0} \frac{ln(x)}{sqrt(x)} Homework Equations Integration by Parts Improper Fractions: Type II Integral (discontinuous at a) The Attempt at a Solution Now, this might seem odd, but I'm having a devil of a time understanding how this is converging when the...

Fractions, Exponents, and x :( I simply just don't get fractions and exponents i was given this problem: [6x^(4/5)-3x(2/3)]/3x^(1/3) i haven't gotten anywhere and I'm stuck help thanks in advance

Homework Statement I need to integrate (2x-5)/(x^2+5x+11) Homework Equations The Attempt at a Solution My problem is just finding a formula for an irreducable quadratic. I know if the denominator was x(x^2+1), I would use A/x+(Bx+C)/(x^2+1). I just don't know the formula in this...

The problem is: ((x^3)+x)/(x-1) And i need to break it into partial fractions... I tried long division and got: ((x^2) +x ) But the book gives me the answer of: (x^2)+x+2+(2/(x-1)) Any help would be very much appreciated, thanks.

Homework Statement Verify that, for all positive values of n, 1/(n+2)(2n+3) -1/((n+3)(2n+5))=(4n+9)/((n+2)(n+3)(2n+3)(2n+5)) For the series ∑_(n=0)^N▒(4n+9)/((n+2)(n+3)(2n+3)(2n+5)) Find The sum to N terms, The sum to infinity. Homework Equations no The Attempt at a...

Okay, I know how to differentiate regular functions. But when it comes to fractions, I'm hopeless. This may be an extremely simple one to some, here is the function; "1/4x-7" I have to differentiate that using the chain rule. I think that u=4x-7, but I am not sure. As i said, I am horrible...

Homework Statement Show that 1/72 cannot be written as the sum of the reciprocals of the squares of two different positive integers. Homework Equations The Attempt at a Solution Available solutions 1/8²-1/24² 1/9²+1/648 Therefore Proven.

Hey. I have a question. What is the packing fraction of a container full of randomly jammed cylinders? Also, does the packing fraction depend on the ratio of the radius to height of the cylinder? There is some contest of finding certain amount of cylindrical objects inside a container (I can't...

Is it possible to calculate the greatest common divisor of decimals and fractions? As far as I know, the greatest common divisor is a number you can calculate for integers, but I wonder if it's possible to calculate it for decimals and fractions.

Can we consider all whole numbers as fraction?why?

Homework Statement I((3x^2+x+4)/(x^4+3x^2+2),x) I((3x^2+x+4)/((x^2+1)(x^2+2)),x) I(3x^2/((x^2+1)(x^2+2)),x)+I((x+4)/((x^2+1)(x^2+2)),x) from here i have used partial fractions with no luck Homework Equations The Attempt at a Solution

Homework Statement partial fractions (-x^2+x+3)/((x-2)^2(x+1)) = A/(x-2) + B/((x-2)^2) + C/(x+1) is my partial fractions set up right A= -1/9 B = 1/3 C=1/9

I'm having trouble understanding what the numerator needs to be in the partial fractions. e.g. \frac{1}{(x-1)(x-2)^2}\equiv \frac{A}{x-1}+\frac{Bx+C}{(x-2)^2} Notice how the first numerator has a constant A, while the second is linear Bx+C. Actually... just now I think I may understand...

Hey guys, I have a quick question concerning partial fractions, say i have the values A(..)+B(..)+C(..) and i can only get A b substituting a value for x, but I can not make A or C go zero or A and B go to zero at the same time, if you understand ? How do I get the values B and C ? I remember...

Is it possible to use partial fractions on exponential factors? An expression like this for example... 3^x ______________________ (2^x + 3^x)(5^x + 6^x) Would it break down into something like this? A^x/(2^x + 3^x) + B^x/(5^x + 6^x) What are the rules for repeated factors...

Homework Statement I need to intergrate the following (4x2+2x-1)/ (x3+x2) How to set up problem using linear factors? The Attempt at a Solution Factoring the denominator I get: x2(x+1) By linear/quadratic factoring I get: A/x + Bx+C/ x2 + d/(x+1) Is this right?

Homework Statement use the method of partial fractions on \int \frac{36}{(x-2)(x-1)^2(x+1)^2} dx [b]2. Homework Equations [b]3. The Attempt at a Solution \frac{A}{(x-2)} + \frac{B}{(x-1)} + \frac{C}{(x-1)^2} + \frac{D}{(x+1)} + \frac{E}{(x+1)^2} I took the 36 out of the...

Homework Statement ∫1/[(x+a)(x+b)]dx answer is 1/(a-b) ln[(x+b)/(x+a)] + C Homework Equations The Attempt at a Solution 1=A/(x+a) + B/(x+b) 1=B(x+a) + A(x+b) 1=Bx+ Ba + Ax +Ab so 0=Bx+ Ax, 1=Ba+Ab A=-B, 1=B(a-b) ∫-1/(x+a) +∫1/(x+b) Im not sure if I am headed in...

Homework Statement Integrate: (x-1) / (X^2 - 4x +5) The attempt at a solution Normally I would try to factor this into something like (x-1) (x+3) (That's an example completely unrelated to this problem.) However, as no easy factors quickly occurred to me I did a run through of the...

\Sigma_{n=1}^{ \infty} \frac{1}{(3n-2)(3n+1)} I simplified it to partial fractions to (1/3) / (3n-2) - (1/3) / (3n+1) Now what?

Homework Statement F(X)=[tex]\int[/\frac{1}{1+t^3} Homework Equations The Attempt at a Solution I have tried different substitutions to find fog where g(t) = ? But am getting stuck

Does the continued product of fractions 1/2 x 2/3 x 3/4 x...x (n-1)/n converge? If so, what does it converge to?

so apparently 3^-1 mod 5 = 2 so (1/3) mod 5 = 2 I don't get how this works, can someone explain?

Homework Statement Actually i want to ask something actually very easy... i just don't know the meaning of some words in different questions... firstly... multiplication of A and B means A*B right? how about multiplication of A by B means A*B or A/B?? secondly... division of A by B means...

Homework Statement I would like to know...when trying to take the derivative of a function with a fraction in it ... should I always turn it into a product and use the product rule, thereby dropping the quotient rule most of the time? Or is the quotient rule needed more so in some cases...

Homework Statement Evaluate the integral: integral (-17e^x-36)/(e^(2x)+5e^x+6 dx Homework Equations partial fractions The Attempt at a Solution Basically, what i did was factored the bottom into (e^x+2) and (e^x+3) because when i expand that, it equals the bottom. From there, i...

Homework Statement I am supposed to evaluate the integral using partial fractions. \int \frac{1}{(x+5)^2(x-1)} dx 2. The attempt at a solution So after doing all the work, I get (-1/36)ln|x+5| - (13/6)ln|x+5| + (1/36)ln|x-1| But the answer in the book appears as (-1/36)ln|x+5| -...

Homework Statement 1/((x^2-1)^2) Homework Equations The Attempt at a Solution so i get (Ax+B)/(x^2-1) + (Cx+D)/((x^2-1)^2) then i multiply both sides by ((x^2-1)^2) then i get 1=(Ax+B)(x^2-1)+ (Cx+D) then i multiply it out Ax^3+Bx^2 -Ax +Cx +D =1 then i equate...

10.00 + 00.11 = 10.11 ...am i right? how about if.. 0.1 + 0.1 = ? is it equal to 1.0 ? thx for helping =)

Homework Statement [(4x-4x2)/x2+2x-3] * [(x2+x-6)/4x] Homework Equations The Attempt at a Solution I'm so lazy, though, I do all this stuff mentally, so... Oby-kaby. I individualized all groups into smaller units(I don't know how to say that in algebrish), by dividing by least...

Homework Statement (3x^2-4)/(x^3-4x-6) Homework Equations I guess integration by parts... But how do i set this up? The Attempt at a Solution The numerator is exponentially lower than the denominator, so no long division. The denominator seems not to factor out into anything...

Homework Statement \int\frac{e^x}{(e^x-2)(e^2x +1)} it should be e to the power of 2x Homework Equations Using substitution u=e^x, and then using partial fractions The Attempt at a Solution I have done this problem two separate ways. One with substitution and then partial...

Homework Statement Solve the integral x/x^2+4x+13 Homework Equations I think that you would use partial fractions but I'm not really sure. I know that you need to complete the square on the denominator. The Attempt at a Solution The completed square would be (x+2)^2+9. I don't...

Homework Statement Simplify \frac{x^2 - \sqrt{x}}{\sqrt{x^5}} Homework Equations Unsure The Attempt at a Solution Tried to factorise the numerator and denominator. Not sure how to proceed given the subtraction in the numerator. Best effort so far...

Homework Statement From the formula t = \frac{L}{v+c} + \frac{L}{v-c} I've made t = \frac{2L}{c}\left(\frac{1}{1 - \frac{v^2}{c^2}}\right). This is the problem: \left(\frac{1}{1 - \frac{v^2}{c^2}}\right) = \left(\frac{1 + \frac{v^2}{c^2}}{1 - \left(\frac{v^2}{c^2}\right)^2}\right) How...

Delete please Please delete. (Edited on Friday 13th 2:53 p.m.) Homework Statement ANYTHING that looks similar to solving these by addition/elimination: Equation One: 3x - y + 2z = 1 Equation Two: 2x +3y +3z = 4 Equation Three: x + y - 4z = -9 The book's answers: (-1, 0, 2) The...

Homework Statement Integrate x^3 + 49 / x^2 + 5x + 4 Homework Equations The Attempt at a Solution Since the numerator has an x cubed, but the denominator only has an x squared, I know I need to divide the numerator by something. I'm not sure what, but maybe the...

Homework Statement The problem asks to evaluate the integral using partial fractions, but I just cannot find out which trick to get this one to work. the equation is \int\frac{x^3+x^2+2x+1}{(x^2+1)(x^2+2)} The Attempt at a Solution I have tried setting it up as a partial fraction...

i'm trying to write the equation dB=log_10(P_2/P_1) I just need help writing this equation into Fortran. I know for exponents I use **, but what about subscripts? Also, my inital thought for a fraction is /. Is this correct?

Homework Statement Split the function into partial fractions. 1/(w^4-w^3)Homework Equations 1/(w^4-w^3) The Attempt at a Solution I started by factoring the denominator to w^3(w-1) and re-writing the original function as (Aw^2+Bw+C)/w^3 + D/(w-1) and set it = 1/(w^3(w-1)) I end up with...

What do I do when a decimal or a fraction is found only within the parentheses in a linear equation? I know about the general removal process; but my question involves equations like these: 17(2.33 - x) - 35(4 - 30x) = 2 7(4/3 - x) + 24(5x - 60) = 31 Should I distribute first and then get...

Homework Statement integrate (4x^2 + 3x + 6)/x^2 (x+2) dx Homework Equations don't have sorry.. The Attempt at a Solution firstly = A/x + B/x^2 + C /x+2 , = A(x^2)(x+2) + B(x)(x+2) + C(x)(x^2) equating with the 4x^2 + 3x + 6,then i integrate it,but my ans turn out to be...

I can't seem to make the brackets cover the full fraction when stating a differential, namely \begin{equation} (\frac{df}{dt}) \end{equation} Any tips?

I've been working with Laplace Transforms and integration ALOT lately. Many times I windup having to use partial fractions to solve the problem and frankly my algebra skills just aren't up to the task. Take this fraction for example; I know 3 ways to do it... 1 of the ways doesn't work unless...

\frac{s-1}{s(s-2)^2} How can I expand this fraction? \frac{A}{s} + \frac{B}{(s-2)} + \frac{C}{(s-2)^2} right? This gives me the equation As^3 - 6As^2 + 12As - 8A Bs^3 - 4Bs^2 + 4Bs + Cs^2 - 2Cs = s-1 so that (1) A + B =0 (2)- 6A - 4B + C = 0 (3) 12A + 4B - 2C = 1 (4)...

Expressing fractions as powers?? How would you go about expressing this 127/squareroot(5) as a power of 5? I got a copy of last years exams to use for revision and practice and its full of stuff I don't know how to do. This one happens to be a multiple choice and the possible answers are 5 to...

\int e^{ax}cosbx This one is driving me insane. So I used e^ax as u and cosbx dx as dv. And then I did it again using e^ax as u and sinbx as dv which left me with \int e^{ax}cosbx = \frac{1}{b}e^{ax}sinbx + \frac{a}{b^{2}}e^{ax}cosbx - \frac{a^{2}}{b^{2}}\int e^{ax}cosbxdx I have no...

Homework Statement How does one integrate e.g. \frac{1+x}{(2+x)^{3/2}} by partial fractions? The Attempt at a Solution I have no idea about this. I've never seen this technique applied with fractional powers before.

Homework Statement Derive a formula for the antiderivative of sec x using the identity that sec x= cos x/ (1-sin^2x). Use a substitution for sin x and then partial fractions. Then multiply the solution by (1+sin x)/ (1+sin x) to obtain the more familiar formula for the antiderivative...