Thursday, 22 October 2015

trigonometry - How lim $h->0$ $sin h/h$ is equal to $1$?

›
How $\lim_{h\to 0} \sin h$ when divided by $h$ gives the value $1$ ? Does it also follows with other ratios that for example. $\l...

Proof verification : $X_n to X$ in distribution, $Y_n to 0$ in probability $implies$ $X_nY_n to 0$ in probability

›
I have to show : $X_n \to X$ in distribution, $Y_n \to 0$ in probability $\implies$ $X_nY_n \to 0$ in probability. Let $\alpha>0, \epsi...
Wednesday, 21 October 2015

real analysis - Is the sequence of functions $f_n=chi_{[n,n+1]}$ uniformly integrable?

›
I wish to prove or disprove that the sequence of functions $f_n=\chi_{[n,n+1]}$ is uniformly integrable? At a glance my judgement is YES, it...

intuition - Math Courses involving clever integration techniques

›
I am a third year undergraduate mathematics student. I learned some basic techniques for simplifying sums in high school algebra, but I have...

logarithms - How to solve exponents using log?

›
How can I solve an exponent in a equation using base 10 logarithm tables? For an example, $$a = b^x$$ can be written as $$ \log_{10} a= x\lo...

real analysis - $sumlimits_{n=1}^infty log(1+a_n)$ converges absolutely $iffsumlimits_{n=1}^infty a_n$ converges absolutely.

›
$$\sum\limits_{n=1}^\infty \log(1+a_n) \text{ converges absolutely} \Leftrightarrow \sum_{n=1}^\infty a_n \text{ converges absolutely}.$$...

number theory - Show that $3p^2=q^2$ implies $3|p$ and $3|q$

›
This is a problem from " Introduction to Mathematics - Algebra and Number Systems " (specifically, exercise set 2 #9), which is on...