Recent content by aPhilosopher

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    Proving f(x) ≡ 0 with given conditions |f'(x)| ≤ M|f(x)| for 0 ≤ x ≤ L

    updated my last message
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    Proving f(x) ≡ 0 with given conditions |f'(x)| ≤ M|f(x)| for 0 ≤ x ≤ L

    I thought I had a proof but I tried to do it in my head and made a stupid mistake. It is interesting to note that |f'(x)| ≤ M |f(x)| implies that |f'(x)| ≤ (M + N)|f(x)| with 0 ≤ N. If we let U = M + N for arbitrary N then we can work with a constant that's arbitrarily large instead of M. The...
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    Does the inverse distribute over the group operation o?

    I think what office shredder was asking is "Does the inverse distribute over the group operation o?" In other words, does (xoy)-1 = x-1oy-1 or does it equal something else?
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    Is the Set of 3x3 Matrices Annihilating a Given Vector a Subspace?

    To show that it's a subspace, you have to show that if it contains u and v, then it contains au + bv where a and b are scalars, that it contains 0 and that it contains -u for any u that it contains.
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    Finding Solutions for Simultaneous Equations Involving Trigonometric Functions

    Let's try another way. What's the determinate of the system? For what values of a is it zero? There's a mistake being made in the algebra somewhere and I'm not in the mood to sort it out.
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    Finding Solutions for Simultaneous Equations Involving Trigonometric Functions

    When does cos a = 0?
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    Finding Solutions for Simultaneous Equations Involving Trigonometric Functions

    I think that you're paying far too much attention to the fact that you have trigonometric coefficients. This is a system of linear equations in the variables x and y. Why are you solving for the coefficients? Solve for x and y. Then look and see where the solutions you get are defined.
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    If integral equals zero, then function equals zero

    I messed up, you don't want to take \epsilon < d but some fraction of d. 1/2 is convenient. then f > d/2. But c - \delta < x < c + \delta gives you an interval for which f(x) > d/2
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    Proving the Theorem: A, B, C, and D Vectors | Step-by-Step Guide

    There's one more relevant equation. As a hint, think of AxB as an additional vector V.
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    If integral equals zero, then function equals zero

    You don't have to get that involved with it. Just choose \epsilon < d to begin with.
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    Finding Parallel and Orthogonal Vectors for u and v

    Are you sure that there are no relevant equations? What about those defining defining parallel and orthogonal?
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    Matrix A^2 = 0, then A + I is nonsingular. Proof?

    Very nicely explained Hurkyl. I like that perspective.
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    Calculating period of a function

    Now that you put them next to each other, it does look like pi. I don't think that the function is periodic of period 1 either in that case.
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    Calculating period of a function

    3t is only specified as the value of f on the interval [0, n] where n is the period of f.
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    Calculating period of a function

    what's the definition of periodicity that you've been given?