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  1. M

    Just another limit problem

    You should have 0/0 not 6/0. In any case, try a trick similar to what you did with the radical in the denominator.
  2. M

    Partition on R^3

    In both cases equivalent points lie on the same plane (sphere). What are the equations of these planes (spheres)?
  3. M

    Conjugates in the normalizer of a p-Sylow subgroup

    OK solved, if anyone wants to see solution let me know.
  4. M

    Conjugates in the normalizer of a p-Sylow subgroup

    Well, let me put up some more of what I have found - still no solution. Since a,b \in Z(P) we know that P \subseteq C(a) and P \subseteq C(b). Since P \subseteq N(P) we also know that P \subseteq N(P) \cap C(a) and P \subseteq N(P) \cap C(b) . Further, x^{-1} C(a) x = C(b)...
  5. M

    Conjugates in the normalizer of a p-Sylow subgroup

    [SOLVED] Conjugates in the normalizer of a p-Sylow subgroup Homework Statement Let P be a p-Sylow subgroup of G and suppose that a,b lie in Z(P), the center of P, and that a, b are conjugate in G. Prove that they are conjugate in N(P), the normalizer of P (also called stablilizer in other...
  6. M

    Math proof

    What's the remainder on division by 3 of the 3 factors you have exhibited?
  7. M

    Differentiating with multiple variables

    One way would be to substitute for x and y, which would result in a function of t alone.
  8. M

    Curve of Intersection in two Three-Dimensional EQs

    What kind of sadistic prof assigned this?
  9. M

    Natural Logs+Calc related question

    Halls, the OP seemed to be the problem you mention but the original image that she uploaded was the other one, so I think it's ok. The poster just needs a bit more care in where parentheses go.
  10. M

    Operations on sets

    I don't quite understand what you mean when you say X/B is not a union of X/A. Can you clarify please?
  11. M

    Find the Maclaurin series for f(x) = (x^2)(e^x)

    The main point is just that every polynomial is its own Taylor Series, irrespecitve of about what point it is taken. It will always come out to be itself.
  12. M

    Find the Maclaurin series for f(x) = (x^2)(e^x)

    The process wouldn't differ, i.e. if you wanted to take the Taylor Series of a polynomial about x = a you would evaluate all your derivatives at x = a instead of at x = 0. As an example, if I took the Taylor series of the general 3rd degree polynomial at x = 1 I'd have f (1) = A + B + C + D...
  13. M

    Integral of tan(x)^3

    1 + tan^2 = sec^2 is not equivalent to 1 - sec^2 = tan^2? (step 2) Looks like you missed a negative sign, pretty small error that apparently got magnified later on.
  14. M

    Find the Maclaurin series for f(x) = (x^2)(e^x)

    Here's an example: Take the Maclaurin series of f(x) = Ax^3 + Bx^2 + Cx + D (degree 3 polynomial) f(0) = D f ' (x) = 3*Ax^2 + 2*Bx + C so f ' (0) = C f '' (x) = 3*2*Ax + 2*1*B so f ''(0) = 2!B f ''' (x) = 3*2*1*A so f ''' (0) = 3!A f ''''(x) = 0 (and all higher derivatives as well are...
  15. M

    Find the Maclaurin series for f(x) = (x^2)(e^x)

    It only requires finding derivatives and evaluating them at x = 0. When the original function is a polynomial I am hopeful that you find taking a derivative to be a piece of cake!
  16. M

    Intersection of 2 planes

    Are you familiar with the cross product? If so, consider the cross product of the normals to each plane. By the way, what if the planes are parallel?
  17. M

    Find the Maclaurin series for f(x) = (x^2)(e^x)

    It's pretty clearcut. Just follow the recipe for building a Maclaurin series for a polynomial of the general form, and lo and behold the answer will be the original polynomial.
  18. M

    Natural Logs+Calc related question

    How would you find the "slope of a line that is tangent to the graph"? Once you have the slope, what point would lie on the tangent line if it is tangent to the graph? Once you have the slope, and a point, how do you get the equation of the line?
  19. M

    Find the Maclaurin series for f(x) = (x^2)(e^x)

    Any polynomial in x would be it's own Maclaurin series, just so you know.
  20. M

    Find the Maclaurin series for f(x) = (x^2)(e^x)

    Looks like you missed something. Edit: you're post was initially blank.
  21. M

    Curve of Intersection in two Three-Dimensional EQs

    I was looking at this, but I'm not sure that the method can work as nicely here (the author says there's no foolproof method) http://www.asaurus.net/~buhr/academic/2004-1-ubc-math263/handouts/curve.pdf
  22. M

    Curve of Intersection in two Three-Dimensional EQs

    Above you aren't using the spherical definition for z. Edit: Hmmm, this is harder than I thought, hope I didn't bring you to a dead end. I'll keep working on it. Edit 2: Somehow you need to combine the two equations together to get something like U^2 + V^2 = constant^2, at which point you...
  23. M

    Curve of Intersection in two Three-Dimensional EQs

    Now the tricky part. You need to eliminate a parameter so that your curve of intersection expresses the set of points of the intersection with one parameter (this way it's a curve rather than a surface).
  24. M

    Vector spaces: column spaces

    Can b be expressed as a linear combination of the columns of A? If the system is consistent, well...
  25. M

    Uniqueness of a vector

    So, x_3 is the 3rd component of x correct? If that's the case (I don't see what else it could be) then I agree that it doesn't seem to be unique as we have (1) x_1 = -15 + 10t (2) x_2 = -3 (3) x_3 = t Now t can be chosen to be any real number. Are you sure that you copied them correctly?
  26. M

    Curve of Intersection in two Three-Dimensional EQs

    The next step you should work on is parametrizing the plane. Can you do this?
  27. M

    Curve of Intersection in two Three-Dimensional EQs

    First, think about it. Do you know what kind of surfaces each of these are? If so, do you see how they can intersect?
  28. M

    Spivak's Calculus on Manifolds problem (I). Integration.

    Does the boundary of C have content zero? That may be the angle to start from (at least for the implication that assumes C is Jordan-measurable).
  29. M

    Set Theory Proof

    Looks like you got the jist.
  30. M

    Set Theory Proof

    :approve: A picture should help with the proof. Draw a circle with x and y at random points and x0 at the center. Then try to fit the triangle inequality in with your picture.
  31. M

    Set Theory Proof

    If |x-x0| < r you can think of it as saying that the disk of radius r about x0 encloses the set. What can you then conclude?
  32. M

    Set Theory Proof

    For clarity, x is supposed to be any element of A correct? If so, then think about using the triangle inequality if it's available.
  33. M

    Bounded set proof

    That's more like it, but the fact that x lies in the union simply means that |x| < max (m,n) which I would call K.
  34. M

    Bounded set proof

    You are proving a statement about A U B, so you need to start with an arbitrary element in A U B. You can then invoke the known properties of A and B individually to prove the statement regarding the union.
  35. M

    Bounded set proof

    You should really start by assuming that x is in A U B. Then say why there is a constant K such that |x| < K.
  36. M

    Classification of groups of order 8

    You want to show H is a normal subgroup of G not the reverse. Showing that H is a subgroup follows from the fact that y has order 4. Do you see why? To show it's a normal subgroup of G consider the left (or right) cosets of H in G. How many are there?
  37. M

    Inner Automorphisms as a Normal Subgroup

    This is good \tau is a mapping and \tau^{-1}(g) is an element of the group on which the mapping is defined. Your question is not making sense. You have successfully shown that that the inner automorphisms are normal in the group of automorphisms. You can stop there.
  38. M

    Limits of integration

    Maybe you should break the integral up into the part over t < 0 and t > 0. What does that turn into? I don't know the answer, just a suggestion.
  39. M

    Limits of integration

    The substitution introduces dx = 2t dt within the integral. Perhaps a polar coordinate form would be helpful.
  40. M

    Differential Eq. (Substitution)

    I think you need to check that again.
  41. M

    Linear Algebra Dual Basis

    Each basis vector in V that satisfies fi(ej) = \delta ij defines a system of 3 equations in 3 unknowns. Each of these systems gives you one of the basis vectors.
  42. M

    Constant that makes g(x) continous over (-inf,inf)

    Well, yeah, thinking is always good, but he *thought* he should try the quadratic formula and I think he's right in the sense that it will give him the correct answer.
  43. M

    Constant that makes g(x) continous over (-inf,inf)

    Quadratic formula sounds like a good place to start.
  44. M

    Open sets

    What are the original sets that comprise the union? They can't be open individually if you are being asked that very question.
  45. M

    Vector Analysis Help

    I believe this calls for the method of Lagrange multipliers?
  46. M

    Limit problem, is this right?

    Sounds like you reversed the directions.
  47. M

    Algebraic Countability

    Show...? You forgot to put in the statement.
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