Amaths / Pure Chemistry

77th Cloud SG

Amaths

How do I Integrate X^-1?

Chemistry

Why is mercury's melting/boiling point different from other metals?

Maybe i'm not trying hard enough, but cant seems to find the answers in google.

tanjun SG

Pertaining to your A maths qn, please do note that when differentiating ln x, you will get x ^-1.

Since integration is a reverse process of differentiation, therefore, integrate x^-1 and you will get ln x + c which c is a constant.

Runawaylove SG

Mercury's bonds = stronger than the other metals? That's why need more heat to break the bonds and more heat to form bonds?

I think so Very Happy

tanjun SG

for your chem qn, u can try out this link

http://www.madsci.org/posts/archives/may97/862179191.Ch.r.html

77th Cloud SG

Runawaylove, Metals have high boiling/melting point except for Group I and II metals, AND mercury, thus it wouldn't be higher. And, why are the bonds weaker, in that case?

Amaths question: BUT, if i do the normal way, [x^0]/0, isn't that not defined?

Darkness_hacker99 SG

The atomic orbital is not the in syllabus of O level Pure Chemistry.

Y_Shun SG

x ^-1

= ln x ?

77th Cloud SG

Yeah, It’s not in the syllabus. My teacher told me to ‘find it out myself’ if i wanna know, and well, I wanna know =.=

tanjun SG

Nope. It is like a formula that you have to memorise. If u wanna know more like how cum differentiate ln x will become x^-1, you will have to use differentiation using first principle which is longer.

eagle SG

not only is it longer, it is not within O level syllabus. But to use it, you must really understand what exactly is differentiation. O levels only teaches you how to use it, but not exactly why it is used like that...

tanjun SG

It is commendable that you have a "want to know more" attitude. Keep up with the good work.

^tamago^ SG

You can't do the normal way. Mathematicians found that they could not integrate 1/x so...

http://en.wikipedia.org/wiki/E_%28mathematical_constant%29#e_in_calculus

tanjun SG

Thanks for the info. I have learnt a new thing too. Laughing