If f(x) = 0 for all nonzero x and f(0) = some constant c, how can you show that lim = 0 for any x as x approaches a?
I tried using the definition of limit, but this is going nowhere.
Consider two machines, both of which have an exponential lifetime with mean 1/λ. There is one repairman who can service machines at an exponential rate of μ.
How does one set up the Kolmogorov backward equations for such a scenario? I am not sure after finding the rates how to work those...
Consider two sequences, {a_n} and {b_n}.
If there is a one-to-one correspondence between these sets, can we conclude anything about their behavior considering, say, that we know that one is convergent?
Going further, can we conclude anything about the series resulting from these sequences?
I am having a hard time finding a starting point for these problems. One is to find a sequence with subsequences that converge to 1, 2, and 3.
A similar problem (which would solve both problems) is to find a sequence that has subsequences that converge to every positive integer.
I am not...
I.e., what is beneficial about main(int argc,char *argv[])?
I see a lot of seemingly good programmers write the main like this, but what does it do that int main() cannot do?
I recently built a new computer off newegg. Put everything together without a hitch, and order Windows 7 oem. I proceeded to install windows 7. Once the download was complete, I went to use my mouse, it didn't work. I figured this as being no big deal seeing as how I did not install my...
I sometimes try to think about the relationship that exists in theory between a supposed god and us, the products of this god. The idea of a god implies that this is a being far beyond the scope of human intelligence and the laws of our physical world, so doesn't it seem a bit absurd to believe...
Given that we humans are descended from the great ape, as well as are gorillas and chimpanzees and bonobos, why do we have hair that grows indefinitely, while they do not? I've read something about a sexual selection aspect to evolution, surmising that hair is a means to finding a mate, like...
lists = [(2 * i + 1) for i in range(100)]
i = 0
while (i < 100):
if(lists[i] == 3):
lists.remove(lists[i])
i = i + 1
print lists
It is giving me an error about the index being out of range. I am new to python and I am not understanding this error.
Edit: Fixed it. This is by...
I hope someone will give me some of his/her time and help me understand this--and given the platform, I'd say the more math in your explanation the better. I am having some trouble understanding a particular type of hedging ones investments: say that company X is going down the tubes and you...
For a function
using namespace std;
mst(const vector<list<pair<int,int> > > &adj_lists, int v){
// code before iterator
list<pair<int,int> >:: iterator it;
it = adj_list[0].begin();
// code after
}
I'm trying to set up an iterator to walk through the list contained within...
Say you have an even function f(y) (that is, f(y) = f(-y)) and you want to integrate
\int_ \infty^0 yf(y) dy
From negative infinity to 0 (sorry, latex wasn't doing what i wanted)
Is it allowed to take the limit to infinity in the positive direction, and negate the y...
I am working on a proof in which I have an integral with bounds negative infinity to zero, with an even function, i.e., f(y) = f(-y). I took the limit to infinity rather than negative infinity since y is negative (which is OK I think) but now I have an integral that goes from infinity to 0. What...
I'm trying to create a full adder using one 3-to-8 decoder and some nand gates. As of now I know I will have X, Y, and C_in as my inputs. I am having trouble with figuring out what the 8 outputs of the decoder should be, so I am unsure about where and how to use the nand gates. Anyone able to...
A 65.1 kg person jumps from rest off a 3.04 m-high tower straight down into the water. Neglect air resistance during the descent. She comes to rest 1.11 m under the surface of the water. Determine the magnitude of the average force that the water exerts on the diver. This force is...
How can I find probability p that maximized P(Y = y*) when Y has a negative binomial distribution with parameters r (known) and p? I've just reduced the problem with some algebra, but other than guess-and-check I have no rigorous way to solve this problem.
Suppose that Y is a random variable with moment-generating function m(t) and W = aY + b, with a moment-generating function of m(at) * e^(tb). Prove that V(W) = V(Y) * a^2. I have done an absurd amount of work on this problem, and I know its actual solution doesn't have one and a half pages worth...
An insurance company issues a one-year $1000 policy against an occurrence A that happens to 2 out of every 100 owners of the policy. Administrative fees are $15 per policy and not part of the companies profit. How much should the company charge per policy to make a profit of $50 per policy?
I am trying to figure out a way to prove this without using much set theory (i know that the rationals are countable and the reals are not). is there a way to show that there are more reals than rationals in a more straightforward proof?
I've just been messing around on VBA and am trying to write a summation that estimates pi. It doesn't add anything to the sum within the do while. I tried a for loop also, but it just takes whatever i initialize sum to and multiplies it by 4 and adds one. I just want it to add continually to sum...
This is my first attempt at writing a VBA program. I am just trying to square items in excel in column 'A' and output the answer to column 'B'.
Option Explicit
Sub timestimes()
Dim n As Integer
Dim i As Integer
Dim z As Integer
n = Range("A").Count
For i = 1 To n
z =...
I know that everyone says that one should talk to professors after office hours and get to know them and whatnot, but I think I am totally incapable of this. I wish to apply to graduate school in mathematics in the winter and I need three letters of recommendation. I have done some research (if...
Is being able to work effectively with Prolog a worthwhile skill to have? Is Prolog widely used as far as logic programming languages go? Are there any others you might recommend? I am just interested in learning a new, different language after learning some C++ and learning Prolog (or a similar...
I am new to Matlab and have been having problems running a program that has functions defined in seperate files and calls them. I am putting everything onto my flash drive and setting the directory to that, but it gives me an error saying that the input argument in the first function called is...
Homework Statement
Let F be a field with order 2^n. Prove that char (F) = 2.
Homework Equations
The Attempt at a Solution
My reasoning is that since a field is an integral domain, its characteristic must be either 0 or prime. After that I get confused, because would the char (F)...
let G be a group following that whenever a, b and c belong to G and ab = ca, then b = c. prove that G is Abelian.
here is what i have for the proof:
(ab)c = c(ab)
let c = aba^-1 (trying to find a c which which allows for commutativity)
so (ab)aba^-1 = aba^-1(ab)
(ab)aba^-1 = ab(a^-1...
Define T: F^2 --> P_1(F) by T(a, b) = a + bx (with P_1 denoting P sub 1)
I usually prove problems such as this by constructing a matrix of T using bases for the vector spaces and then proving that the matrix is invertible, but is the following also a viable proof that T is an isomorphism...
what i feel a lot of the time about math is not exactly arrogance, but close... i just took my first sorta upper level course in lin. algebra, and i got a d on the first test, a hundred on the second, and now i am unsure about how i did on the final (maybe a b). the sort of arrogance comes from...
let { v_1, v_2, v_3, ... v_m } (m > 3) be linearly independent vectors in a vector space V. Prove that the set { v_1 - 2v_2 + v_3, v_2, v_3, ..., v_m } is also Linearly.
I did this:
a_1( v_1 - 2v_2 + v_3) + a_2(v_2) + a_3(v_3) + ... + a_m(v_m)
= a_1(v_1) - a_1(2v_2) + a_1(v_3)...