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    Integrate [itex]\int_0^1\frac{\sin(\pi x)}{1-x}dx[/itex]

    Thank HallsofIvy. This seems like the most plausible way to handle that imo :biggrin:. Thanks.
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    Integrate [itex]\int_0^1\frac{\sin(\pi x)}{1-x}dx[/itex]

    Oh, I did expand the denominator as a power series and then integrate term by term by resulting series, but I can't proceed to the next step. The general formula for arbitrary k is too complicated for me.
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    Integrate [itex]\int_0^1\frac{\sin(\pi x)}{1-x}dx[/itex]

    Yeah, looks like it yielded some positive results finally , thanks very much for your help.
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    Integrate [itex]\int_0^1\frac{\sin(\pi x)}{1-x}dx[/itex]

    Homework Statement \int_0^1\frac{\sin(\pi x)}{1-x}dx Homework Equations \int \frac{\sin (\pi x)}{1-x}=Si(\pi-\pi x) The Attempt at a Solution I was stuck on the above integral while solving an exercise, I found out earlier on Wolfram that this integral doesn't probably have an elementary...
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    Would it harm my later in life to take calculus 1 online?

    Have a look at this http://www.infocobuild.com/education/audio-video-courses/mathematics/math210-calculus-one-umkc.html. Also check the thread https://www.physicsforums.com/showthread.php?t=349631, which should include many more.
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    Using The Completeness Axiom To Find Supremum and Saximum.

    The field Q is not complete. R is complete. You're supposed to deal with the sup in R. The argument \sqrt{5} is not in Q should only be applied to show that the set aforementioned has no sup over Q.
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    Prove that lim sup(x_n) = max(lim sup(y_n), lim sup(z_n))

    Does this observation help? $\sup {x_n} = \max (\sup {y_n},\sup {z_n})$
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    A collection of audio/video lectures on mathematics

    Calculus Revisited: Complex Variables, Differential Equations, and Linear Algebra. Nice. Prof. Herbert Gross. http://ocw.mit.edu/resources/res-18-008-calculus-revisited-complex-variables-differential-equations-and-linear-algebra-fall-2011/index.htm Downloadable lecture videos and notes.
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    Can one construct a function having the following properties ?

    Is there a function f(x): \mathbb{R} \to \mathbb{R} such that \lim_{x \to 0} x f(x) = a \neq 0.
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    Can irrational numbers exist on the numberline?

    A rational number a/b where b is nonzero can, however, be exactly represented on the real line, can't it?. If irrational numbers didn't exist, then the the number line would have all elements being rational, which can be disproved. Then they must somehow exist :smile:.
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    Advice needed on learning measure theory.

    Do you think having Bogachev's Measure Theory (vol. I) as a first exposure to measure theory sounds a good idea? I mean while I can understand well the concepts presented in the book, I find some techniques used in the proof section quite hard to follow. :confused:
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    How many exercises do I have to complete ?

    I'm taking PoMA-Rudin, do I have to complete all the exercises after every chapter to be regarded as understanding the material ? Does all the tools for solving the exercises lie in the material? Because I feel many problems require more than the textbook. Thanks.
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    Calculate the antiderivatives

    Thank you very much, I can take it from here :D.
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    Lattice points on a circle.

    Thanks, I didn't think thoroughly before posting this silly question, sorry.
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    Lattice points on a circle.

    Ah, my bad :tongue:, I meant to ask if EVERY circle having irrational radius have no lattice points on its boundary, not an example :smile:.
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    Lattice points on a circle.

    Thanks, but the equation x^2 + y^2 =1/2 seems to have no integer solution...
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    Lattice points on a circle.

    Does any circle having irrational radius have no lattice points on its boundary ? Extended question: Is there any way to determine the number of lattice points lying on the boundary of a given circle ? *The centres of these circles are all (0,0) *
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    Calculate the antiderivatives

    Actually my original problem was determining the convergence or divergence of the following improper integral: \int^{+∞}_{0} \frac{ln(x^{2}+4^{x})}{\sqrt{3x^{7}+7x^{^3}}}dx I split the integral into \int^{+∞}_{1} \frac{ln(x^{2}+4^{x})}{\sqrt{3x^{7}+7x^{^3}}}dx and \int^{1}_{0}...
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    A finite set and convergence

    Idea: Establish a bijection f: N -> A n |-> f(n)=x_{n} If there exists no N: \forall n > N, x_{n} = const, then A must be infinite -> hence we obtain a contradiction. :smile:
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    Calculate the antiderivatives

    Homework Statement \int \frac{ln(x^{2}+4^{x})}{\sqrt{3x^{7}+7x^{^3}}}dx Homework Equations X. The Attempt at a Solution Wolfram Alpha seem to give no answer.
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    Small confusion about an improper integral example.

    Thanks, I was just confused when my answer doesn't match the exercise's solution, maybe some mistakes were made . Thank again :biggrin:.
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    Small confusion about an improper integral example.

    Thanks but I'm wondering why they used the first one instead of the second. lim_{\stackrel{}{t \rightarrow 0^{+}}}\int^{1}_{t}\frac{1}{\sqrt{1-x^{2}}} lim_{\stackrel{}{t \rightarrow 1^{-}}}\int^{t}_{0}\frac{1}{\sqrt{1-x^{2}}}
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    Small confusion about an improper integral example.

    We have that \int^{1}_{0}\frac{1}{\sqrt{1-x^{2}}}=lim_{\stackrel{}{t \rightarrow 0^{+}}}\int^{1}_{t}\frac{1}{\sqrt{1-x^{2}}}=lim_{\stackrel{}{t \rightarrow 0^{+}}}[arcsin(x)]^{1}_{t}=\frac{\pi}{2} However, I think \int^{1}_{0}\frac{1}{\sqrt{1-x^{2}}} should equal to lim_{\stackrel{}{t...
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    On an example of neighborhood.

    guess I misunderstood some of the concept in the first place, I thought the ball centered at 1 must completely lie in the interval [1/2,1]. :D. Thank guys.
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    On an example of neighborhood.

    Hi folks, as I was reviewing the metric space section in Amann- Escher textbook, I came across the following example of neighborhood: "For \left[0,1\right] with the metric induced from R, \left[\frac{1}{2},1\right] is a neighborhood of 1, but not of \frac{1}{2}." However I can't point out the...
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    Help on lim sup and lim inf

    Never mind, I grasped the idea at last :biggrin: , but thanks aw.
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    Simplifying equations. Orders of operation.

    This should do it :biggrin:
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    Help on lim sup and lim inf

    Hi everyone, I'm currently having problems with these concept, my textbook states that: Let S be the set of all subsequential limits of s_n, then sup S= limsup s_n inf S= liminf s_n Knowing that S is also the set of all limits point of s_n, however I'm wondering how I could determine this...
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