You said choose something that's larger than the sequence but easier to deal with...
@HallsOfIvy: Not sure exactly how to work with that at the moment but I'll see what i can do with that approach.
@Ray Vickson: I don't know if I'm allowed to use any limit laws...the question asks says to...
Ok I chose 2n (arbitrarily, I'm not aware of any other set criteria for choosing the value) and after a bit of algebra I ended up with $$\left|\frac{(-1)^n}{n}\right|<1$$ which I think is the same as the 'rather trivial' inequality I was asking about.
But so, after choosing a value, where...
I think so...
|\frac{1}{n}-0|< \epsilon
\frac{1}{n}< \epsilon
n>\frac{1}{\epsilon}
So if n is greater than 1/ε, then 1/n will be within ε of 0. So we can take N=1/ε and that would mean if we want to be within ε of 0 then take n to be some larger number than N=1/ε (just a bit of thinking...
Homework Statement
Prove that the sequence a_n=\frac{1}{n}+\frac{(-1)^n}{n^2} converges to 0 using the definition of convergence.
The Attempt at a Solution
I'm pretty stumped on this one...all I've written is |\frac{1}{n}+\frac{(-1)^n}{n^2}-0| < \epsilon
The only way I know how to...
I recently found an app for Macs called 'SelfControl' which let's you block certain websites for a certain amount of time (up to a day). Even if you restart your computer, you'll still be blocked until the timer runs out.
The problem I still have is that there's so many videos and saved...
Thanks...could you please elaborate a bit on what 'vacuous' means in this context?
EDIT: Nevermind, I wiki'd it and think I understand it. Of course, any additional thoughts would be appreciated.
Could someone please explain why PQ in the diagram below is rΔθ? Isn't rΔθ arc length?
The best reason I can think of is that it's only an approximation for when the angle is very small, so PQ≈arclength=rΔθ. Not 100% sure though.
http://imageshack.us/scaled/landing/199/feynmanangle.jpg...
If we have a set of two elements, say S={0. 1} and we defined 0 to be less than 1, would this obey the transitivity axiom? (If a<b and b<c then a<c? )
To me, it seems looks like you need at least 3 elements but I'm not entirely sure.
What if I don't take an average temperature for the ocean and use the value listed for boiling water? Wouldn't this assume that the water at the surface is 'behaving' like boiled water which is why 1 gram is evaporating for every 2.3kJ or fenergy absorbed?
So would it then just be ~2.3kJ/g multiplied by the mass evaporated?
If so, does this assume that the forces on the water molecules at the surface is equal to the intermolecular forces on water molecules when they're boiling...which is why they require the same energy to evaporate? :confused:
Yes, it's defined on my sheet as 'the amount of energy in joules required to transform one gram of liquid water into water vapor at the boiling point of water'..
So should I be just looking at this energy rather than include the energy required to bring the surface of the water up to the...
Homework Statement
Calculate how much energy is required to evaporate 3.6x10^14kg of water.
(Original question is that if the oceans cover about 70% of the Earth's surface and an average of 1m evaporates per year, find the the energy required to evaporate the calculated amount of water...
Sorry for the late reply, I've been a bit occupied with coursework.
I'm not sure how you knew to replace the original integrand with arctan(yx) evaluated from y=1 to y=π