Recent content by nicnicman

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    Difficult simplification for Arc length integral

    Okay thanks for the help everyone
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    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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