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    Assume that f is a continuous, real-valued function

    Assume that f is a continuous, real-valued function defined on a metric space X. If {xn} is a sequence in X converging to x, prove that Limn→∞f(xn) = f(x). Here is my attempt, but I am not sure if it is correct.
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    I Concept behind equivalent metrics

    Ok, here is one example. Take two metrics d1 and d2 Would these two metrics be equivalent?
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    I Concept behind equivalent metrics

    Well i'm taking Advanced Calculus 1, so it's only topological concepts of metric spaces and not a whole lot on topological spaces in general.
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    I Concept behind equivalent metrics

    My professor never really went over this concept clearly in Advanced Calculus. The definition of an equivalent metric from my lecture slides: Two metrics: d1 and d2 on a metric space X are called equivalent when there exists M >= 1 such that M-1d1(x,y) <= d2(x,y) <= Md2(x,y) I am trying to...
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    Courses Which course should I take: Discrete Math or Bridge to Advanced Mathematics?

    Just a question, do all universities require students (especially math majors) to take an intro to mathematical proof class in order to take advanced, proof based math classes?
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    Courses Which course should I take: Discrete Math or Bridge to Advanced Mathematics?

    These courses are at two different colleges that I plan on going to (whichever picks me). I think that discrete math is more relevant for Computer Scientists and the other for Math majors. But both look similar (for the bridge to advance math course, it does teach you to write proofs, something...
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    Courses Which course should I take: Discrete Math or Bridge to Advanced Mathematics?

    Hi, I am currently an undergraduate student and I plan on taking advanced math courses such as Abstract Algebra, Real Analysis, Complex Analysis, etc. There are two courses which I think could help me prepare for the courses above as they are proof intensive: discrete math and bridge to advance...
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    Courses Is proof based Linear Algebra be similar to Abstract Algebra

    I haven't really went deep into physics because I just started Physics, but definitely plan on taking more advanced physics courses, but from what I researched, people divide physics into experimental and theoretical, the latter being more math. Also, from what I heard, physicists are not...
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    Courses Is proof based Linear Algebra be similar to Abstract Algebra

    Thanks for your reply. So essentially a proof based Linear Algebra course would be the same level of difficulty as an Abstract Algebra and the proofs, though different, are not so difficult. As for physics, I would think proof based math classes like Abstract Algebra are not that useful in...
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    Courses Is proof based Linear Algebra be similar to Abstract Algebra

    I know both are different courses, but what I mean is, will a proof based Linear Algebra course be similar to an Abstract Algebra course in terms of difficulty and proofs, or are the proofs similar? Someone told me that there isn't that much difference between the proofs in Linear or Abstract...
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    Courses What other chemistry courses use the periodic table?

    Ok maybe every chemistry course uses it. For my organic chemistry class, I just needed to know a few elements, electronegativity, and atomic numbers, but other than that, there was no use of the periodic table. Gen Chem II, It was the same thing. but we never looked at the periodic table. I...
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    Courses What other chemistry courses use the periodic table?

    So far, I have taken General Chemistry I and II, and Organic Chemistry I. Out of these classes, only General Chemistry I seems to make use of the periodic table, but it is mostly just going through the basics of the periodc table. Not so much in Gen Chem II or Orgo I. I mean they give it to you...
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    I Zeros of sines and cosines

    But I want to know the whole step. Do I get the values by just looking at their domains from their graphs?
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    I Zeros of sines and cosines

    Just a quick question, I was solving sin(x)=0 and cos(x)=0. I was trying hard to find out the solutions and the solutions were: for sin(x)=0------>x=0, pi, 2pi for cos(x)=0-------->x=pi/2, 3pi/2 But my question is why are those the solutions?
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    Help with solving Laplace Transform problem

    Homework Statement Solve Laplace Transform L{tsin(2t)sin(5t)} Homework Equations cos(bt)=s/s^2+b^2 trig identity (product identity): sin(a)sin(b)=1/2[cos(a-b)-cos(a+b) t^nf(t)=(-1)^nd^n/ds^nF(S) (the template is complicated for me to use. Srry for the inconvinience) The Attempt at a Solution...
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    Differential Equation: x^2y''-xy'-3y=2x^-(3/2)

    Homework Statement Homework Equations The Attempt at a Solution I am not asking to find the answer, just wanted to know whether to use the variation of parameters or undetermined coefficients. Because this was on a test problem and I used variation of parameters instead. I know it is a...
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    Please help with this Differential equation problem

    My professor did not go in dept. I just know know: if a constant: yp=A if x: yp=Ax+B if x^2: yp=Ax^2+Bx+C if cos(x) or sin(x): yp=Acos(x)+Asin(x) if e^x: yp=Ae^x Or something like that???
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    Please help with this Differential equation problem

    But I need to know why instead of using yp=ae^4x, you have to use yp=axe^4x (sorry, the template to write the equation like you did is very complicated for me)
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    Please help with this Differential equation problem

    Homework Statement y''-16y=2e^4x. Find general solution Homework Equations The Attempt at a Solution I have the homogenous equation which is c1e^-4x+c2e^4x, but I'm trying to find the particular solution for 2e^4x. I did yp=ae^4x, yp'=4ae^4x, yp''=16ae^4x, then plugged it into the equation...
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    Calculus III (help sketching graph)

    Homework Statement Sketch the curve with the given vector equation. Indicate with an arrow the direction in with 't' increases r(t)=<t, 2-t, 2t> Homework Equations parametric equation (can't type the equation, too confusing to use the template) The Attempt at a Solution So far, I have <1...
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    I Calculus III (sketching graph)

    Sketch the curve with the given vector equation. Indicate with an arrow the direction in with 't' increases r(t)=<t, 2-t, 2t> So far, I have <1, -1, 2> and points (0, 2, 0). Am I even correct? And how do I sketch the graph. I know it's suppose to be in the xyz graph, but how do I graph the...
  22. R

    Need help solving Differential Equation

    Thanks, I know how to do it now. :smile:
  23. R

    Need help solving Differential Equation

    Thank you for the link. It translates automatically into any language so it's ok. I wanted to know the whole steps on how to solve the integral: sin(3x)/cos^2(3x) (I found the template, but don't know how to use it yet. I don't go on that much on these forums for help. It's my first time using...
  24. R

    Need help solving Differential Equation

    Again, So far, I have ∫2ydy=-∫sin(3x)/cos^2(3x)dx. Is that right? If so, how do I integrate -∫sin(3x)/cos^2(3x)?
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    Need help solving Differential Equation

    These are practice questions for elementary differential equations. Oh...I just realized that there was a typo. It's: Sin(3x)dx+2yCos^2(3x)dy=0
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    Need help solving Differential Equation

    Sin(3x)dx+2ycos(3x)dy=0 So far, I have ∫2ydy=-∫sin(3x)/cos^2(3x)dx. Is that right? If so, how do I integrate sin(3x)/cos^2(3x)?
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    Question about Organic Chemistry and Physical Chemistry

    Why, is Greek complicated? :oldeyes:. It does all sound confusing and intimidating to people who are just beginning Orgo. From what I heard from others taking it, you have to be able to both memorize and understand why. There are people who just memorize without understanding anything at all...
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    Question about Organic Chemistry and Physical Chemistry

    For Organic Chemistry, all I can think of is having to remember: methane, hexane, butane, propane, octane, pentane, nonane, decane, ethylene, methylene, etc, etc o0) You also have to remember the formula and have to draw a very complicated spider web-like bonding structure :oldeek:. I feel like...
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    Question about Organic Chemistry and Physical Chemistry

    So the topics I need to really focus on for Organic Chemistry are: General Chemistry I: Electronic Structure of Atoms, Periodic Properties of Elements, Basic Concepts of Chemical Bonding, Molecular Geometry and Bonding Theories. General Chemistry II: Chemical Kinetics, Chemical Equilibrium...
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    Question about Organic Chemistry and Physical Chemistry

    I've heard from a lot of people who took Organic Chemistry in my college as well as on other forums that there is not that much General Chemistry involved in Organic and it only involves bonding, electronegativity and more on memorization and understanding how chemical reactions work than in...
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