Recent content by grothem

Homework Statement Determine the transfer function between output x and input F for the following mass-spring system. (see attached image) Homework Equations F=ma Inertia, T = J \alpha Rotational Damper, T=B \omega Rotational Spring, T=K \theta The Attempt at a Solution I'm having...

Homework Statement An infinite quantum well width is 5 nm. An electron is confined in the well with 50% in the lowest eigenstate E1 and 50% in the second lowest state E2. 1. What is the energy difference between the two lowest states, E2-E1 2. What is the possible wavefunction of the...

ok. So arctan(x) = \int\frac{1}{1+x^2} = \int\sum (x^(2*n)) = \sum\frac{x^(2(n+1)}{2(n+1)} is this what you mean?

Homework Statement Evaluate the indefinite integral as a power series and find the radius of convergence \int\frac{x-arctan(x)}{x^3} I have no idea where to start here. Should I just integrate it first?

Oh ok. So raising ln(5) to power e gives me 5. So sequence converges to 5. Thanks a lot for the help!

ok. The limit of 3^n/5^n = 0 So after dividing through by 5^n, I'm left with ln(5). Which would be a divergent series

I took the natural log and I got: Lim 1/n * ln(3^n+5^n) Then applying L'hospitals: (3^n*ln(3)+5^n*ln(5))/(3^n+5^n) then I simplified from there.

I came up with Limit as n tends to infinity of (ln(3)*(3/8)^n + ln(5)*(5/8)^n) and with those being geometric sequences with r < 1, the sequence is convergent.

oh ok... so I bring the 1/n in front of the ln(5^n*(3/5)^n) now can I just take the limit from there?

so after taking the log I came up with 5(1+(3/5)) = 8. Which I don't think is the right answer, did I do something wrong?

I thought you could only apply the root test to a series, not a sequence, or does it not matter?

Homework Statement Determine if the sequence is convergent or divergent {\sqrt[n]{3^n+5^n}} Homework Equations The Attempt at a Solution I know I need to take the limit to find if it converges or diverges. But I'm not really sure what I need to do to it to take the limit.

Homework Statement Determine if the following is convergent or divergent \Sigma\frac{n+5}{\sqrt[3]{n^7+n^2}} n from 1 to infinity Homework Equations Test for divergence came up with limit = 0 so I know it converges. The Attempt at a Solution Ratio test came up inconclusive...

Homework Statement \int tan^5(6x) sec^3(6x) dx Homework Equations The Attempt at a Solution first off I set u=6x to get 1/6\int tan^5(u) sec^3(u) dx then I used trig identities to put tangent in terms of secant and I came up with \int...

lim sqrt(x^2 + x) - x as x approaches infinity Not sure what I need to do. I tried to make it into a fraction so I could apply L'Hospital's rule but I didnt' get anywhere with that. Any ideas?