Random math questions

[brightsky]

Let y = f(x) = tanhx = (e^x - e^(-x))/(e^x + e^(-x))
To find arctanhx, swap x and y.
x = (e^y - e^(-y))/(e^y + e^(-y))
x (e^y + e^(-y)) = (e^y - e^(-y))
x e^(2y) + x = e^(2y) - 1
(1 - x) e^(2y) = 1 + x
y = 1/2 ln((1+x)/(1-x))
So arctanhx = 1/2 ln((1+x)/(1-x))
So it seems that ln((2+2x)/(1-x)) = 2(ln2 + arctanhx)

EDIT: Error corrected.

[lzxnl]

Let y = f(x) = tanhx = (e^x - e^(-x))/(e^x + e^(-x))
To find arctanhx, swap x and y.
x = (e^y - e^(-y))/(e^y + e^(-y))
x (e^y + e^(-y)) = (e^y - e^(-y))
x e^(2y) + x = e^(2y) - 1
(1 - x) e^(2y) = 1 + x
y = 1/2 ln((1+x)/(1-x))
So arctanhx = 1/2 ln((1+x)/(1-x))
So it seems that ln((2+2x)/(1-x)) = 2ln2 arctanhx

Crap. I knew I forgot something there. However your final step is flawed. You mean 2 (ln 2 + artanh x) right?

[#1procrastinator]

Thanks, I hadn't looked at arctanh yet...I got

[#1procrastinator]

If , and is the complement of in , does ?

Don't know why the tex part isn't working but I'm asking if the union of A and the complement A^c equal to X

[Einstein]

i know this isn't specifically a maths question but, is it good to do say methods a bit every night - like 1 hour or so, even if you have a sac coming up, for say chemistry? cheers

[brightsky]

Crap. I knew I forgot something there. However your final step is flawed. You mean 2 (ln 2 + artanh x) right?

Woops! Of course. Cheers lzxnl!

[kinslayer]

If , and is the complement of in , does ?

Don't know why the tex part isn't working but I'm asking if the union of A and the complement A^c equal to X

Yes. x is in X \ A = A^c if and only if x is in X and x is not in A.

x is in the union of two sets if and only if x is in either one of the sets.

So x is in A union A^c, if and only if 1) x is in X (since A and A^c are both subsets of X) and 2) x is in A, or x is not in A.

2) is a tautology (it is satisfied by any x), so it follows A union A^c is the same set as X.

[idontknow2298]

Can someone please help me with this question?
a positive integer has two digits. The sum of its squares of the digits is 34. The integer formed by reversing the digits is 18 less than the original number. What is the integer?

[RKTR]

53?

[kinslayer]

Can someone please help me with this question?
a positive integer has two digits. The sum of its squares of the digits is 34. The integer formed by reversing the digits is 18 less than the original number. What is the integer?

Let a,b be nonnegative integers and express the number of interest as x = 10a + b

Then a^2 + b^2 = 34 and also 10a + b - 18 = 10b + a, or equivalently, a - b = 2

Solve simultaneously to find a=5, b=3, so that x = 53.

[idontknow2298]

Thankyou!

[idontknow2298]

How about this question:
F ind the mean of x,y and z if 2x+2y+18=4z, in terms of z

[RKTR]

2x+2y=4z-18
x+y=2z-9
Mean=(x+y+z)/3
        =(3z-9)/3
         =z-3

[idontknow2298]

Of course! Thank you so much ^_ ^

[#1procrastinator]

How do you evaluate ? Tried L'hopital's rule but ended with something like and differentiating top and bottom just gives pretty much the same thing