Recent content by Byeonggon Lee

Thanks. Definitely better to use the definition than contrapositive.

Yes you're right. I edited the post. converse of the theorem: $$ \lim_{n\to\infty} a_n = 0 \Longrightarrow \lim_{n\to\infty} |a_n| = 0$$ I tried to prove it by using contrapositive contrapositive of the converse: $$ \lim_{n\to\infty} a_n \neq 0 \Longrightarrow \lim_{n\to\infty} |a_n| \neq 0$$ I...

This theorem is from the stewart calculus book 11.1.6 If $$ \lim_{n\to\infty} |a_n| = 0$$, then $$\lim_{n\to\infty} a_n = 0$$ I wonder whether converse of this theorem true or not

Of course 1 isn't same as -1. This proof must be wrong but I can't find which part of this proof is wrong. Could you help me with this problem? (1)$$1 = \sqrt{1}$$ (2)$$= \sqrt{(-1)(-1)}$$ (3)$$= \sqrt{(-1)} \cdot i$$ (4)$$= i \cdot i$$ $$=-1$$

I need to prove whether this expression is true or false: ## \sum\limits_{k=1}^{n}\int_{k-1}^{k}[x]dx = \frac{n(n-1)}{2} ## I'm so confused because as I know, definite integral is possible only when the target function is continuous in closed interval. In this case, function ##[x]## should be...

Unfortunately my book seems extremely disorganized ... no details about this. Only this theorem exists in the corner of a page. Thanks I read the article in purple math, and see some videos in youtube.

Thanks for replying ! My book also introduced partial fraction decomposition which is ##\frac{1}{AB} =\frac{1}{B-A}(\frac{1}{A}-\frac{1}{B})## But this following expression is so complicated that I can't apply partial fraction decomposition. ##\frac{2x+6}{(x−1)(x+1)^2}## Could you explain to...

You can also use u-substitution as phion said## \int\frac{-2x+20}{\sqrt{-x^2+20}}dx ## As you can see -2x+20 is derivative of -x^2+20 And if you substitute -x^2+20 with variable such as t, then the problem becomes simpler ## t=-x^2+20x ## ## \frac{d(t)}{dt} = \frac{d(-x^2+20x)}{dt} ## ##...

Hi I'm currently doing 'integral by substitution' part in a book. Although it is integral by substitution part, some exercises are solved using reduction of fraction and integral, without substitution. (Actually I can't solve some exercises if I use substitution and the book's explanation also...

I only memorized these trigonometric differential identities : `sin(x) = cos(x) `cos(x) = -sin(x) because I can convert tan(x) to sin(x) / cos(x) and sec(x) to 1 / cos(x) .. etcAnd there is no need to memorize some integral identities such as : ∫ sin(x) dx = -cos(x) + C ∫...

From the definition of trigonometric function cos=x/r sin=y/r From the Pythagorean theorem r^2=x^2+y^2 cos^4(x) + sin^4(x) =(x^4+y^4)/r^4 =((x^2+y^2)^2-2x^2y^2)/(r^4) =(r^4-2x^2y^2)/r^4 !=1

Thanks, I'll try it

Hello I recently noticed that mathematical logic is related to computer science. I haven't studied math in university yet I'm not good at math and Since I'm not a native English speaker some English is hard to me. Is there any good and easy book which describes mathematical logic used in...

Truth table aha! thanks

Hi :smile: I am studying mathematical logic by a pdf file. But there is no proof about this therorem so I don't understand.. How to prove this?