Recent content by grothem

Homework Statement Linearize the equation Vout = (10^v)*sin(x) about x=0,0.1, and 1. Write the equation in both the original coordinates and the shifted (linearized) coordinates.Homework Equations y=f(a)+f'(a)(x-a)The Attempt at a Solution dVout/dx = (10^v)*cos(x) evaluating that equation...

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 A point source of monochromatic light (500 nm) is 50 cm from an aperture plane. The detection point is located 50 cm on the other side of the aperture plane. a) The transmitting portion of the aperture plane is an annular ring of inner radius .5 mm and outer radius .935...

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...