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Original post by number23
Any maths people out here who can help me with some uni maths prep? :redface:


Certainly. But, you would get a more speedy response if you created your own thread :wink:
Original post by boromir9111
Certainly. But, you would get a more speedy response if you created your own thread :wink:


have done :smile:

does anyone know why arcsinxx2+1=arctanxarcsin\frac{x}{\sqrt{x^2+1}} = arctanx ?

its for an integration question! thanks
Reply 3842
Avatar for SimonM
SimonM
18
Consider a right angled triangle with sides, x, 1, sqrt(x^2+1)
Original post by SimonM
Consider a right angled triangle with sides, x, 1, sqrt(x^2+1)


thanks. so does the equation only exist in some cases (right angle triangles with a side=1)?
Reply 3844
Avatar for davros
davros
16
Original post by number23
thanks. so does the equation only exist in some cases (right angle triangles with a side=1)?


No, but you can always change your measurement scale so that the opposite side = 1 unit!!
Reply 3845
Avatar for davros
davros
16
Original post by number23
...



Original post by Oh my Ms. Coffey
I was working on my preuniversity workbook and came across this

'Expand (1+x+x^2)^6 to the power x^4 by writing it in the form (1+(x+x^2))^6'



I take it you two are both preparing for Durham? I'm seeing the same sorts of questions crop up in different places!!
Original post by davros
I take it you two are both preparing for Durham? I'm seeing the same sorts of questions crop up in different places!!


Yeah mine was from the work book, I dont know if the other person's was I couldnt even attempt those sorts of questions (I think its further maths).
Reply 3847
Avatar for nohomo
nohomo
5
Let Z\mathbb{Z} denote the set of all integers. Determine (with proof) all functions f:Z→Zf: \mathbb{Z} \to \mathbb{Z} such that for all x,yx,y in Z\mathbb{Z}, we have f(x+f(y))=f(x)−yf(x+f(y)) = f(x)-y.
Original post by nohomo
Let Z\mathbb{Z} denote the set of all integers. Determine (with proof) all functions f:Z→Zf: \mathbb{Z} \to \mathbb{Z} such that for all x,yx,y in Z\mathbb{Z}, we have f(x+f(y))=f(x)−yf(x+f(y)) = f(x)-y.


solution



EDIT: Not sure why the question is restricted to the integers; the argument is practically the same for the reals, too.
(edited 11 years ago)
Reply 3849
Avatar for Zuzuzu
Zuzuzu
12
All I know about mathematics is how to add and multiply, and that 21=22^1 = 2 and abac=ab+ca^ba^c = a^{b+c}. Find the minimum number of calculations required to find 21002^{100}.
could someone please explain how to work out the answer to these 2 questions.

http://imageshack.us/f/577/screenshot20121028at191.png/

http://imageshack.us/f/844/screenshot20121028at190.png/
Calculate lim⁡n→∞(∏k=1n(n+kk))1n2\displaystyle \lim_{n \to \infty}\bigg( \prod_{k=1}^{n} \binom{n+k}{k}\bigg)^{\frac{1}{n^2}}.
Reply 3852
Avatar for SimonM
SimonM
18
Original post by L'art pour l'art
Calculate lim⁡n→∞(∏k=1n(n+kk))1n2\displaystyle \lim_{n \to \infty}\bigg( \prod_{k=1}^{n} \binom{n+k}{k}\bigg)^{\frac{1}{n^2}}.


Spoiler

(edited 11 years ago)
Original post by SimonM

Spoiler

Brilliant! :hat2:


Use a clever little algebraic maneuver to evaluate ∫1212x7−8(x7+x+4)2  dx\displaystyle \int_{1}^{2} \frac{12x^7-8}{(x^7+x+4)^2}\;{dx}.

Hint

Spoiler

Original post by L'art pour l'art


Use a clever little algebraic maneuver to evaluate ∫1212x7−8(x7+x+4)2  dx\displaystyle \int_{1}^{2} \frac{12x^7-8}{(x^7+x+4)^2}\;{dx}.

Hint

Spoiler



I like... :wink:
It had me for a while. I got it from an old calculus textbook. :wink:

Spoiler


(edited 11 years ago)
Show that dndxn(11+x2)=(−1)nn!sin⁡[(n+1)θ]sin⁡n+1θ\displaystyle \frac{d^n}{dx^n}\left(\frac{1}{1+x^2} \right) = (-1)^nn!\sin[(n+1)\theta]\sin^{n+1}{\theta} where x=cot⁡θ.\displaystyle x = \cot{\theta}.

(It had a hint with it in the book, but people on TSR are too good so I left it out :tongue: -- ask if you're stuck).
Could someone recommend a graphical calculator for use of FP2 and FP3 please :biggrin:

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