4U Revising Game (1 Viewer)

[Drongoski]

Mr harism

Thank u. In my hurry, I dropped the x^n. I've amended my solution.

 

[Trebla]

Would've been much simpler if you just do:



Question:

Suppose f(x) = 1/x + sin²(πx) / πx². By considering the first derivative, prove that f(x) is decreasing for x > 0.

 

[Drongoski]

Trebla

Certainly a cleaner solution.

 

[harism]

yea i see drongoski.
its a nice solution.
(call me haris, lol)

btw, trebla.
my god.
gurmies was right about you.
your epic.

i would never have seen that solution coming. =O
good work!

 

[gurmies]

Hey Treb, is x a whole number? Sure would help...

 

[harism]

Hey Treb, is x a whole number? Sure would help...

would help indeed.

 

[azureus88]

[maths]f'(x)=-\frac{1}{x^2}+\frac{1}{n}\frac{2nx^2\sin(nx)\cos(nx)-2x\sin^2(nx)}{x^4}\\=-\frac{1}{x^2}+\frac{1}{n}\frac{nx\sin(2nx)-2\sin^2(nx)}{x^3}\\=\frac{-nx+nx\sin(2nx)+\cos(2nx)-1}{nx^3}\\=\frac{nx(\sin(2nx)-1)+(\cos(2nx)-1)}{nx^3}\\<0\,\,$for$\,\,x>0\\$since$\,\,-1\leq \sin(2nx)\leq 1\,\,$and$\,\,-1\leq \cos(2nx)\leq 1\\$and when$\,\,\sin(2nx)=1,\cos(2nx)\neq 1[/maths]

 

[gurmies]

[maths]f'(x)=-\frac{1}{x^2}+\frac{1}{n}\frac{2nx^2\sin(nx)\cos(nx)-2x\sin^2(nx)}{x^4}\\=-\frac{1}{x^2}+\frac{1}{n}\frac{nx\sin(2nx)-2\sin^2(nx)}{x^3}\\=\frac{-nx+nx\sin(2nx)+\cos(2nx)-1}{nx^3}\\=\frac{nx(\sin(2nx)-1)+(\cos(2nx)-1)}{nx^3}\\<0\,\,$for$\,\,x>0\\$since$\,\,-1\leq \sin(2nx)\leq 1\,\,$and$\,\,-1\leq \cos(2nx)\leq 1\\$and when$\,\,\sin(2nx)=1,\cos(2nx)\neq 1[/maths]

I think it's pi, not n...?

 

[harism]

Would've been much simpler if you just do:



Question:

Suppose f(x) = 1/x + sin²(πx) / πx². By considering the first derivative, prove that f(x) is decreasing for x > 0.

trebla, put us out of our misery.
is it a pi or an n?

thanks.

 

[omniscience]

everyone on this site is shit. they cannot solve my question

 

[shaon0]

everyone on this site is shit. they cannot solve my question

stfu

 

[omniscience]

stfu

no u

 

[shaon0]

no u

lol, u got me

 

[omniscience]

lol, u got me

for ur shitness in maths

 

[shaon0]

for ur shitness in maths

no.

 

[hermand]

everyone on this site is shit. they cannot solve my question

?

 

[gurmies]

Sorry, but who is this guy? Sif no ban yet..

 

[Drongoski]

trebla, put us out of our misery.
is it a pi or an n?

thanks.

Don't think it's pi; trebla is not in the habit of making such a typo.
Provided n > 0 it's all ok. So azureus88's solution stands.

 

[GUSSSSSSSSSSSSS]

Don't think it's pi; trebla is not in the habit of making such a typo.
Provided n > 0 it's all ok. So azureus88's solution stands.

much agreed xD

 

[harism]

Don't think it's pi; trebla is not in the habit of making such a typo.
Provided n > 0 it's all ok. So azureus88's solution stands.

its not a typo, drongoski.
check it yourself... copy what looks like an 'n' and paste it into word. you will see its a pi, not an n.

i had mistaken it for an 'n' myself. But it was gurmies who knocked some sense into me.