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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

    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?

    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 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?

    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

    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

    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...
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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

    Hi. I have a question about Organic and Physical Chemistry. I have already finished General Chemistry I and II and got decent scores on both of them (B on both of them). I am interested in taking Organic Chemistry, then Physical Chemistry afterwards. I know that both are different from General...