Recent content by TaylorWatts

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    MATLAB Plotting multiple polynomials in matlab

    Ok, I can plot a single polynomial easy enough such as 3*(x^2)-1 using fplot, but I want to graph multiple polynomials. When I try to use the plot it doesn't work even for one though. The graph is completely wrong. ie I make a new m-file. x = [-1:1]; y = 3*x.^2 - 1; Then call the...
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    Lebesgue Integrable Function question

    Homework Statement Let f be a Lebesgue integrable function in the interval [a,b] Show that: lim integral from a to b (f(x)*|cosnx|) = 2/pi * integral from a to b (f(x)) n->infinity Homework Equations Every measurable function can be approximated arbitrarily close...
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    Isomorphisms between cyclic groups? (stupid question)

    Why is Z mod 2 x Z mod 3 isomorphic to Z mod 6 but Z mod 2 x Z mod 2 not isomorphic to Z mod 4?
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    Inner Prod Space, Positive Definite Proof

    Homework Statement Let H be an inner product space. Let T:H->H be a linear, self adjoint, positive definite operator. Fix h in H and let g = T(h) / square root (1 + (T(h),h)). for h in H Show that the operator S:H->H defined by S(v) = T(v) - (v,g)g for v in H is positive definite...
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    Number of subgroups of S4

    Not a true homework question, but I'm trying to find all subgroups of S4. Including the identity and the group itself, I've found 30. Is that correct? I've got groups such as: trivial s4 alternating group {identity, (12)}, {identity, (13)} etc - 6 of these {identity, (123), (132)}...
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    Basic question regarding continuous inverses

    Regarding the definition of homemorphism, when we say a function is a homeomorphism if it is continuous, bijective, and has a continuous inverse I assume that means over the codomain only. For example if we have a map from f: R -> (0,1) does f inverse need to be continuous on (0,1) only?
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    Binding an integral Rudin 6.14

    Homework Statement Let f(x) = integral [x to x+1] (sin(e^t)dt). Show that (e^x) * |f(x)| < 2 and that (e^x) * f(x) = cos (e^x) - (e^-1)cos(e^(x+1)) + r(x) where: |r(x)| < Ce^-x, C is a constant Homework Equations integration by parts The Attempt at a Solution Well...
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    Rudin - a notational question

    It's problem #16 for Chapter 6 if anyone answering has the book handy. [x]/x^s + 1. What does he mean by [x]?
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    Some Analysis proofs (complete, just need a check)

    Homework Statement Suppose f >= 0, f is continuous on [a,b], and {integral from a to b} f(x)dx = 0. Prove that f(x) = 0 for all x in [a,b] Homework Equations The Attempt at a Solution Suppose there exists p in [a,b] s.t. f(p) > 0. Let epsilon = f(p) / 2 > 0. The...
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    Another Analysis question: continuity and compactness

    Let I = [0,1] be the closed unit interval. Suppose f is a continuous mapping from I to I. Prove that for one x an element of I, f(x) = x. Proof: Since [0,1] is compact and f is continuous, f is uniformly continuous. This is where I'm stuck. I'm wondering if I can use the fact that since...
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    L'Hopital's Rule: Advanced Analysis

    I see my mistake. Thanks!
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    L'Hopital's Rule: Advanced Analysis

    I did. The problem is if f ' (x) = |x| then f '' (0) does not exist, but neither does: lim [f (0 + h) + f (0 - h) - 2 f (0)] / h^2, unless I am missing something here??? h->0
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    L'Hopital's Rule: Advanced Analysis

    I tried both absolute value of x and square root of x and still get 0/0 or if I apply l'Hopital's Rule I get infinity. Which also means the limit does not exist.
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    L'Hopital's Rule: Advanced Analysis

    Suppose f is defined in a neighborhood of x, and suppose f '' (x) exists. Show that: lim [f(x+h)+f(x-h)-2f(x)] / h^2 = f''(x). h->0 Show by an example that that the limit may exist even if f '' (x) may not. (hint: use lHopital's Theorem). Proof: f '' (x) exists implies...
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