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    Big-Oh Notation

    Homework Statement Determine the complexity of the following code: for (i = 0; i < 2*n; i += 2) { for (j=n; j > i; j--) { a++; } } The Attempt at a Solution Well.. The first for block is O( n ) because i is incremented by 2 each loop up to 2n. The second block...
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    Combinatorics Class - Sum Question

    Or will it be \sum\limits^n_{i=0} \dfrac{\dbinom{n}{i}}{n!} I'm confused as to whether the sum is still involved.
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    Combinatorics Class - Sum Question

    So the answer I'm looking for is \frac{\dbinom{n}{i}}{n!} Correct?
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    Combinatorics Class - Sum Question

    Homework Statement For any positive integer n determine: \sum\limits^n_{i=0} \frac{1}{i!(n-i)!} Homework Equations I don't really know where to start.. Up until this point we've just been doing permutations, combinations, and determining the coefficient of a certain term in the expansion of...
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    Sum of Series

    Ah, perfect. I love you guys, you're so helpful. I guess I need to be a little more critical of my own work though, before I give up on what I've done completely. Now though, knowing A & B (I guess I was solving for them wrong), I am still confused as to how to get the 'nth term' of a series...
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    Sum of Series

    Alright, well this is what I've done: \frac{6}{n(n+1)} = \frac{A}{n} + \frac{B}{n+1} \frac{6}{n(n+1)} = \frac{A(n+1) + Bn}{n(n+1)} 6 = A(n+1) + Bn 6 = An + A + Bn Split into two equations, 1: 6 = A + B 2: 6 = A Then, 2->1: 6 = 6 + B B = 0 I can see I'm doing something wrong, because...
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    Sum of Series

    Alright, I've separated the equation into the following: \frac{6}{n(n+1)} = \frac{A}{n} + \frac{B}{n+1} And solved for A, B, getting A = 6, B = 0. So, I'm left with: \sum\limits^\infty_{n=1} \frac{6}{n} Now, I'm lost as to what to do. I don't know how to solve for this sum... Any hints...
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    Sum of Series

    Homework Statement Evaluate the sum of the following: \sum\limits^\inf_{n=1} \frac{6}{n(n+1)} Homework Equations The Attempt at a Solution Well... The denominator is going to get infinitely large as n approaches infinity, so would the value of the sum not converge to zero? The...
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    Comparison Test: Am I using a good comparison function?

    Homework Statement Does the following interval diverge? \int^9_1 \frac{-4}{\sqrt[3]{x-9}} Homework Equations The Attempt at a Solution Well.. I've used the following function that I think is always less than the above function to prove that the function above DOES NOT diverge (by...
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    Partial Frac. Decomp. Integral ( long div? )

    Got it! Thanks guys, I owe an infinite amount of thanks to PhysicsForums..!
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    Partial Frac. Decomp. Integral ( long div? )

    Homework Statement \int^1_0 \frac{-3x^3+12x+30}{x^2-x-6}dx Homework Equations The Attempt at a Solution I've attempted long division, but the long division does not seem to come to an end.. I'm not sure what to make of this.. If the long division does not end, does this mean that...
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    Integral (Partial-Frac Decomp) SIMPLE?

    Integral (Partial-Frac Decomp) **SIMPLE? Homework Statement \int^3_2 \frac{-dx}{x^2-1} Homework Equations The Attempt at a Solution = \int^3_2 \frac{A}{x} + \frac{B}{x-1} dx For some integers A and B. -1 = A(x-1) + B(x+0) -1 = Ax - A + Bx Split into two equations...
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    Trig Identity Integral

    Homework Statement I missed one class on trigonometric identities in integrals, and I feel that one is needed here: \int^3_0\frac{1+arctan(\frac{x}{3})}{9+x^2}dx Homework Equations The Attempt at a Solution Again, I'm unsure what to do. I think that it is a trig identity, but I could be...
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    Derivative of an Integral

    So the answer would be, -\frac{sin(x^2)}{x^2} \cdot 2x Is this now correct?
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    Derivative of an Integral

    Homework Statement Find the derivative of the function F(x) = \int^0_{x^2-1}\frac{sin(t+1)}{t+1}dt Homework Equations The Attempt at a Solution F'(x) = -\frac{sin(x^2)}{x^2} I'm just learning this and unsure if this is correct. It seems too easy?
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    Definite Integration by Substitution

    Homework Statement \int^2_1 6x\sqrt{x-1}dx Homework Equations The Attempt at a Solution Let u=x-1. Then, u+1=x, and du=dx. Continued from problem statement, =6 \int^1_0 (u+1)u^{\frac{1}{2}}du =6 \int^1_0 u^{\frac{3}{2}} + u^{\frac{1}{2}}du =6(1^{\frac{3}{2}} + 1^{\frac{1}{2}}) =6(2) =12...
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    Integration by Substition

    Homework Statement \int \frac{-2x}{\sqrt[4]{x+2}}dx The Attempt at a Solution =-2*\int x(x+2)^{\frac{1}{4}}dx Let u=x+2. Then, u-2=x, and du = dx .. Continued from above, =-2*\int (u-2)u^{\frac{1}{4}}du =-2*\int u^{5/4}-2u^{\frac{1}{4}}du Is that last step allowed?
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    Differential Equation Involving Natural Log.

    Homework Statement Calculate the following: \int^{-4}_{-6} (x^-1+5x)dx Homework Equations The Attempt at a Solution I've worked this down to ln(-4) + 5(-4) - ln(-6) - 5(-6) =ln(-4)-ln(-6)+10 The answer to the left half (the ln parts) of the equation is undefined, and the...
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    Discrete Counting Question

    No, they're restricted to one prize each.
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    Discrete Counting Question

    Homework Statement How many was can 3 identical prizes be awarded to 98 potential winners? Homework Equations The Attempt at a Solution Well. I know that if the prizes were unique, the first prize would have 98 possible winners, the second prize would have 97 possible winners...
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    Discrete Relations: can't understand relation definition

    If anyone has anything close to an idea of what this could mean.. Please help. I just need a good guess so I can try the question, but I don't have a clue.
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    Discrete Relations: can't understand relation definition

    Homework Statement Let Z be the set of all integers. Then, S is a relation on the set Z x Z defined by: for (a1, a2), (b1, b2) belong to Z x Z, (a1, a2)S(b1, b2) <-> a1b2 = a2b1. Homework Equations The Attempt at a Solution The actual problem is about symmetry...
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    Integral of x(e^x)

    Homework Statement What is the integral of x(e^x)? The Attempt at a Solution It's part of a larger question. I've got a midterm tomorrow and just realized I don't know the principles of integrating e^x other than that the integral of e^x is e^x. I've scoured my textbook and cannot find...
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    Comparison Test on Interval 0 to 1

    Homework Statement Determine whether or not the integral from 0 to 1 of (5ln(x)) / ( x^(3/2) ) converges or not. Homework Equations The Attempt at a Solution I just need to know which end of the integral they are talking about. As x=>0, y=>-infinity. As x=>1, y=>1. I'm assuming...
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    Comparison Test: converges or diverges?

    Homework Statement Determine whether or not the improper integral from 0 to infinite of (e^x)/[(e^2x)+4] converges and if it does, find it's definite value. Homework Equations The Attempt at a Solution I missed the lecture on the Comparison Test, so I'm essentially useless. I...
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    Basis for kernel space

    Thanks heaps hallsofivy, that cleared things up for me. Wish me luck on my exam!
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    Finding determinant with upper triangular matrix

    Thanks heaps for all the help guys, that got my issue cleared up!
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    Basis for kernel space

    Homework Statement Find a basis for the kernel space of the following matrix: -1 -2 -1 2 2 -2 -4 -4 10 2 1 2 2 -5 2 -1 -2 0 -1 0 row reduce to 1 2 0 1 0 0 0 1 -3 0 0 0 0 0 1 0 0 0 0 0 Somehow read the solution as { [-2 1 0 0 0]T, [-1 0 3 1 0]T } .. I don't...
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    Finding determinant with upper triangular matrix

    Perhaps I'm understanding how to reduce to upper triangular form wrong. This first one comes from my Professor, so I'm assuming it is right: 0 2 1 -3 2 1 3 6 9 3 6 9 (rearrange rows) -3 2 1 0 2 1 1 2 3 (r1 / 3) -3 2 1 0 2 1 1 2 3 0 8 10 (r2 + 3(r1)) 0 2 1 1 2 3 0 2 1...
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    Finding determinant with upper triangular matrix

    So. I've been told by my prof that the best way to find the determinant of a matrix is to row reduce it to upper triangular and then take the product of the numbers on the diagonal. That's fine, BUT, how do you know how to reduce it? Depending on what row operations you do, you get...
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