Recent content by danielatha4

"mv = d/dt (1/2 mv^2)" Do you mean... mv = d/dv (1/2 mv^2) ?? wouldn't d/dt (1/2 mv^2) = mv(dv/dt) ?

n integrations of ln(x): x^n[ln(x)-(1/n!)(S)] where S is the sigma sum of 1/k where k=1 to n

Homework Statement Can this equation be solved for x? This isn't any type of homework. I'm doing this for fun. This equation came from an integration while solving a differential equation.

looks good to me

Yeah, looks right to me. Thanks for the help.

I did manage to get this far int/ sec^2A cscA = int/ (tan^2A + 1) cscA = int/ tanAsecA + int/ cscA = secA + int/ cscA is this right? isn't the integral of cscA equal to ln| tan x/2 | ?

Oh ok, I see that now. Thanks. I'll try a different way of solving this problem.

d/dA cscA = -cotAcscA so dcscA = -cotAcscA dA d cscA/-cotA = cscA dA cscA/cotA = secA -dsecA = cscA dA Which step is wrong?

I'm currently trying to find the length along function of ln(x) for the heck of it. I set up this integral for length L= int/ sqrt(1+(y')^2) so y'=1/x so the integral becomes int/ sqrt(1+(1/x^2)) = int/ sqrt(x^2+1)/x So I used trig substitution. I set tanA=x...

Actually if you set it up as ln(y) = x ln(x) You would only have to prove the derivative of ln(x), product rule, and implicit differentiation. You can prove d/dx ln(x) by setting up e^(lnx)=x and using implicit differentiation, and the derivative of e^x which is easily done with the...

Homework Statement I've been challenging myself with finding tricky derivatives lately, and I'm stuck with this one. Does anyone have a good way to differentiate x^x? I tried the difference quotient and you used the concept of pascal's triangle to try to simplify terms such as (x+h)^(x+h) or...

Thanks everyone, it makes a lot of sense using simpler methods on easier examples such as e^y=x or e^(lnx)=x lim x-> 0 (1+x)^(1/x) and lim x-> infinity (1+[1/x])^x both being equal to e is still a bit mysterious to me. What does this have to do with? Sequences and series possibly?

Homework Statement I'm trying to prove that d ln(x) / dx = 1/x This isn't a homework problem of mine for any class. I'm just doing it for fun, so if I'm faced with something I'm not sure of, I apologize. I've only made it through Calculus 2 The Attempt at a Solution Difference quotient...

.aaaaaaaaaaaa ... = a/9 .abababababab ... = ab/99 (ab is not multiplication, simply the digits) .abcabcabcabcabc ... = abc/999 (again, not multiplication between a b and c) and so on

Right! 41 from the bottom, 49 from the top. Touche Mythbusters. I'm just glad they didn't just put it at 45 like I initially thought they did.