Recent content by funcalys

Thank HallsofIvy. This seems like the most plausible way to handle that imo :biggrin:. Thanks.

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.

Yeah, looks like it yielded some positive results finally , thanks very much for your help.

Homework Statement \int_0^1\frac{\sin(\pi x)}{1-x}dxHomework 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...

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.

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.

Does this observation help? $\sup {x_n} = \max (\sup {y_n},\sup {z_n})$

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.

Is there a function f(x): \mathbb{R} \to \mathbb{R} such that \lim_{x \to 0} x f(x) = a \neq 0.

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:.

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:

Many thanks :).

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.

Thank you very much, I can take it from here :D.

Thanks, I didn't think thoroughly before posting this silly question, sorry.