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    Difficult simplification for Arc length integral

    Okay thanks for the help everyone
  2. N

    Difficult simplification for Arc length integral

    Thanks for the reply. Yeah I know the dx and dy are backwards...it's just the generic formula we were given. Sorry for any confusion. I did expand the expression under the radical and came up with the same expansion you did, but I still could not see a good way to integrate it. That's...
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    Difficult simplification for Arc length integral

    Homework Statement Find the length of the curve x = 3 y^{4/3}-\frac{3}{32}y^{2/3}, \quad -64\le y\le 64 Homework Equations Integral for arc length (L): L = \int_a^b \sqrt{1 + (\frac{dy}{dx})^{2}} dx The Attempt at a Solution Using symmetry of the interval and the above integral for arc...
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    Integral involving square root and exp

    Okay. I think I've got it. So, \int\frac{dx}{\sqrt{e^{x} + 1}} = \int\frac{2u du}{u(u^{2}-1)} = \int\frac{2du}{(u+1)(u-1)} = \int\frac{du}{u-1} - \int\frac{du}{u-1} = ln|u-1| - ln|u+1| = ln\frac{|u-1|}{|u+1|} where u = \sqrt{e^{x}+1} = ln\frac{\sqrt{e^{x}+1}-1}{\sqrt{e^{x}+1}+1} Thank...
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    Integral involving square root and exp

    Okay. So, \int\frac{dx}{\sqrt{e^{x} + 1}} = \int\frac{2u du}{u(u^{2}-1)} = \int\frac{2du}{(u+1)(u-1)} And now I'm stuck again.
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    Integral involving square root and exp

    Homework Statement \int\frac{dx}{\sqrt{e^{x} + 1}} Homework Equations Using u-substitution The Attempt at a Solution Let u = \sqrt{e^{x} + 1} \Rightarrow u^{2} - 1 = e^{x} Then, du = \frac{e^{x} dx}{2\sqrt{e^{x} + 1}} \Rightarrow dx = \frac{2u du}{u^{2}-1} So...
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    Find a basis for the subset

    Homework Statement Find a basis for the subset S = {(1, 2, 1), (2, 1, 3), (1, -4, 3)} Homework Equations The Attempt at a Solution I'm not absolutely sure I'm doing this correctly but here is my attempt: First, I put the vectors in S in the rows of a matrix (using multiple...
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    Number of functions from one set to another

    Actually I do need help with b). I don't understand what the problem is asking for.
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    Number of functions from one set to another

    Sorry for the delay. a) If n = 1 then there are two choices for the first and only element in the domain. So, we have 2 functions if n = 1 If n = 2 then there are two choices for the first element in the domain. Then, since one choice is taken there is one choice for the second element...
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    Number of functions from one set to another

    Homework Statement How many functions are there from the set {1, 2, . . . , n}, where n is a positive integer, to the set {0, 1} a) that are one-to-one? b) that assign 0 to both 1 and n? c) that assign 1 to exactly one of the positive integers less than n? Homework Equations...
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    Clarification on set of assigned homework problems

    Yeah, now that I look at the problem again I think she just wants us to do every other odd.
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    Clarification on set of assigned homework problems

    Hello everyone, For homework my instructor assigned problem from the book. To show which problems to do she wrote this: 4n + 1 N={1, 2, 3...}. Does this mean problems 5, 9, 13, . . . ? Thanks for any suggestions.
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    Hasse diagram: minimal, least, greatest

    Homework Statement Let S = {2,3,4,5} and consider the poset (S, <=) where <= is the divisibility relation. Which of the following is true? 1. 3 is a minimal element 2. 4 is a greatest element 3. 2 is a least element 4. Both 2 and 3 Homework Equations The Attempt at a Solution My answer...
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    Which posets are lattices

    Homework Statement Could someone help with this problem? Determine which of the following posets (S, <=) are lattices. 1. A = {1, 3, 6, 9, 12} and <= is the divisibility relation. 2. B = {1, 2, 3, 4, 5} and <= is the divisibility relation. 3. C = {1, 5, 25, 100} and <= is the...
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    Partition of Integers with mod

    Just answer yes or no. And, you answered my question. I'm pretty sure the answer is yes. Thanks.
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    Partition of Integers with mod

    Sorry, I forgot to mention this is far from a formal proof. R just means remainder.
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    Partition of Integers with mod

    Homework Statement Are the following subsets partitions of the set of integers? The set of integers divisible by 4, the set of integers equivalent to 1 mod 4, 2 mod 4, and 3 mod 4. Homework Equations The Attempt at a Solution Yes, it is a partition of the set of integers...
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    Digraph walk, path, circuit

    Homework Statement Given the graph, determine if the following sequences form a walk, path and/or a circuit. http://img843.imageshack.us/img843/5686/digraph.png [Broken] 1. a, b, c, e 2. b, c, d, d, e, c, f 3. a, b, c, f, g, a 4. b, c, d, e Homework Equations The Attempt at a Solution 1...
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    Find a matrix that represents the relation

    Homework Statement Find the matrix that represents the given relation. Use elements in the order given to determine rows and columns of the matrix. R on {2, 3, 4, 6, 8, 9, 12} where aRb means a|b. Homework Equations The Attempt at a Solution 1 0 1 1 1 0 1 0 1 0 1 0 1 1 0 0...
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    Symmetric difference of relationships

    Yeah, that would probably help me understand it better. Thanks.
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    Symmetric difference of relationships

    Actually, I defined it as (R1 - R2) ∪ (R2 - R1). How's that?
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    Symmetric difference of relationships

    Homework Statement 2. Let R1 = {(1,1),(1,2),(2,3),(3.4), (2,4) } and R2 = {(1,1),(2,2),(2,3),(3,3),(3,4) } be relations from {1,2,3} to {1,2,3,4} R1⨁ R2 Homework Equations The Attempt at a Solution R1⨁ R2 = {(1,2), (2,2), (2, 4), (3,3)} Is this correct?
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    Relationship: reflexive, symmetric, antisymmetric, transitive

    Yeah, that's what I thought. Thanks for the help again.
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    Relationship: reflexive, symmetric, antisymmetric, transitive

    Homework Statement Determine which binary relations are true, reflexive, symmetric, antisymmetric, and/or transitive. The relation R on P = {a, b, c} where R = {(a, a), (a, b), (a, c), (b, c), (c, b)} Homework Equations The Attempt at a Solution Not reflexive because there is...
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    Relationship: reflexive, symmetric, antisymmetric, transitive

    Homework Statement Determine which binary relations are true, reflexive, symmetric, antisymmetric, and/or transitive. The relation R on all integers where aRy is |a-b|<=3 Homework Equations The Attempt at a Solution The relationship is reflexive because any number minus itself will be...
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    Induction proof with handshakes

    So, was I correct in beginning with 0 rather than 1. To me, it seems to work better.
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    Big-O relationship proof

    Any suggestions?
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