is convergent if and only if p<1 Seems relevant here, And yeah I was a little careless forgetting to change my interval of integration after substituting. With the substitution I actually have:
∫10(eu-1)du/u2 and given this above P condition things are looking divergent to me now.
Dick you...
Homework Statement
Part a.) For a>0 Determine Limn→∞(a1/n-1)
Part b.) Now assume a>1
Establish that Σn=1∞(a1/n-1) converges if and only if Σn=1∞(e1/n-1) converges.
Part c.) Determine by means of the integral test whether Σn=1∞(e1/n-1) converges
Homework Equations
Integral Test
Limit...
yeah you are correct. The question on my assignment is actually written out as cos2n(θ) which really gets on my nerves. Probably more correct that way.
I think i was using the term range incorrectly but I think you know what i was getting at.I was playing around a bit with the values of θ with my calculator. I plugged in a few different θ's that obeyed my "range" for θ to make the series convergent and received different values each time.
When...
Homework Statement
For the following series ∑∞an determine if they are convergent or divergent. If convergent find the sum.
(ii) ∑∞n=0 cos(θ)2n+sin(θ)2n[/B]Homework Equations
geometric series, [/B]The Attempt at a Solution
First I have to show that the equation is convergent.
Both cos(θ)...
Looks like I can't edit my posts?!
I looked at the rest of the problem (That I didn't already post):
2. Derive an expression for the horizontal force F applied to the collar as a function of distance, d and length, L that will result in static equilibrium. Include all free body diagrams...
Sorry that I didn't provide too much legwork on actually solving for anything in this problem. Here is a go at it.
I would like to take a moment to consider all the information I am given.
L is a value that I set (I will solve d in terms of this variable and make graphs on excel)
d is...
Homework Statement
Ends A and B of the 5-kg rigid bar are attached by lightweight collars that may slide over the smooth fixed rods shown in the figure.
The center of mass of the bar is at its midpoint. The length of the bar is 1.5 m. Determine the horizontal force F applied to...
ok so it turns out that i was actually finding more of a square cone (piece of a sphere) rather than an actual cone with a spherical top.
Now taking the comments into consideration i will find where both functions intersect.
After substituting and whatnot I get that the sphere and the cone...
Homework Statement
This is a book problem, as follows: Find the volume between the cone x = \sqrt{y^{2}+x^{2}} and the sphere x^{2}+y^{2}+z^{2} = 4
Homework Equations
spherical coordinates:
p^{2}=x^{2}+y^{2}+z^{2}
\phi = angle from Z axis (as I understand it)
\theta = angle from x or...
ok so i confused the density*dx with density*x. I'm going to have to think about that, for some reason i associated the same x with both the density and the distance. That scares me! :eek:
I am starting to remember that dx = Δx, but it seemed like there was another Δx for the distance. ugh...
ok this is the bit that confuses me.
here's what I did: E = \int\frac{((\lambda0*x0)/x)*x}{x^2} because (\lambda0*x0)/x is a density, and i need a charge, so i need to multiply by x. (x here meaning the xi) And to me that makes sense because that would be the charge value from the small...
Homework Statement
A line charge starts at x = +x0 and extends to positive infinity. The linear charge density varies inversely with distance from the origin, λ(x)=(λ0*x0)/x
derive the expression for the electric field at the origin, E0, due to this infinetly long line-charge (L→+∞)...
gah curse them for using v to denote a speed quantity! :mad:
my head still doesn't want to work properly, but i understand taking the value of Vmax*sin(θ), although I want to write it as Vmax*sin(ωt), from pi to 0.
I guess ωt = radians = θ
And then for some reason i wanted to use the...
Homework Statement
For a particle in simple harmonic motion, show that Vmax = (pi/2)*Vavg where Vavg is the average speed during one cycle of the motion.
Homework Equations
x(t) = A*cos(ωt) (SHM mathematical model)
v(t) = -Vmax*sin(ωt)
Fave = 1/(b-a)∫f(x)dx
The Attempt at a...