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Let X be a topological space and A be an abelian group. Give A the discrete topology. For any open set U of X, Let $\cal A(U)$ be the group of all continuous aps of U into A. Thus with the usual restriction maps we obtain a sheaf $\cal A$.
So, why for every connected open set U, $\cal A(U)\cong A$ for all U?
And, ... |
What is a good reference for the story of congruences such as
$$\tau(n) \equiv \sigma(11)(n)\ mod\ 691$
with a conceptual explanation with connections to \'etale cohomology, etc?
|
What is a good reference for the story of congruences such as
$$\displaystyle \tau(n) \equiv \sigma(11)(n)\ mod\ 691$$
with a conceptual explanation with connections to \'etale cohomology, etc?
|
What is the compelling need for introducing a theory of $p$-adic integration?
Do the existing theories of $p$-adic integration use some kind of analogues of Lebesgue measures? That is, do we put a Lebesgue measure on $p$-adic spaces, and just integrate real or complex valued functions on $p$-adic spaces, or is somet... |
An annuity immediate has quarterly payments of $1000$ for $25$ years at a rate of $6 \%$ converted quarterly. Find its present value.
The effective interest rate $i$ is $0.06/4$. So let $v = \frac{1}{1+i}$. Then wouldn't the present value be $1000 \left(\frac{1-v^{25}}{i} \right)$? |
The paper of Deligne, Formes modulaires et représentations $l$-adiques, available at [numdam][1], explains things well.
[1]: http://www.numdam.org/numdam-bin/fitem?id=SB_1968-1969__11__139_0 |
The paper of Deligne, Formes modulaires et représentations $l$-adiques, available at [numdam][1], has these things.
[1]: http://www.numdam.org/numdam-bin/fitem?id=SB_1968-1969__11__139_0 |
For starters, there are 100 periods, not 25. In your equation, if the interest rate were zero, the present value would be infinite. If you just reduce each payment to present value, what is the value of the nth payment? Can you then sum this from 1 to 100? |
I want to find the volume of a torus with a given thickness and a given radius.
Let r be the radius of a circle with its midpoint at $M(0|b)$ ($b \geq r$). Now I want to rotate this circle about the x-axis, that is to say about a circular path which has the length $2 \pi \cdot |b|$. So I thought I'd simply integrate... |
For starters, there are 100 periods, not 25. If you just reduce each payment to present value, what is the value of the nth payment? Can you then sum this from 1 to 100? |
If $\ln(1-x+x^2) = a_1x+a_2x^2 + \cdots \text{ then } a_3+a_6+a_9+a_{12} + \cdots = $ ?
My approach is to write $1-x+x^2 = \frac{1+x^3}{1+x}$ then expanding the respective logarithms,I got a series (of coefficient) which is nothing but $\frac{2}{3}\ln 2$.But this approach took some time for me (I can't solved it du... |
**Rewritten**
Okay: first, you need to know what the operations are on $V$.
The simplest way is to start by thinking about the set $\mathbf{V}$ of *all* linear transformations from $\mathbb{R}^4$ to $\mathbb{R}^2$ first. If you already know this is a vector space and under what opeartions, skip the next paragraph... |
$\textbf{EDIT:}$
**So Mike has proved that $S(n)$ in fact diverges.**
**The conjecture is now that $\displaystyle \lim_{n \rightarrow \infty} (2 \log_{2}(n) - S(n)) = \alpha$ where $\alpha \approx 0.667$.**
Look at http://math.stackexchange.com/questions/11726/limit-of-sn-displaystyle-sum-k1-infty-left1-prod-j... |
**Re-rewritten**
It seems, from your comments, that you aren't even very comfortable with the idea of the set $V$ as a vector space.
As it happens, it is better to start from a bit further back, and consider the set of **all** linear transformations from $\mathbb{R}^4\to\mathbb{R}^2$, which I'm going to call $\ma... |
**Re-rewritten**
It seems, from your comments, that you aren't even very comfortable with the idea of the set $V$ as a vector space.
As it happens, it is better to start from a bit further back, and consider the set of **all** linear transformations from $\mathbb{R}^4\to\mathbb{R}^2$, which I'm going to call $\ma... |
How can I proof that dividing an irrational number by an irrational number (besides himself) **can** result in an integer? |
Proof that dividing irrational number by an irrational number can result in an integer? |
By giving an example. For instance, $2\sqrt{2}$ divided by $\sqrt{2}$?
*Note well:* To prove that something **can** happen, all you need to do is exhibit a single instance of it happening. To prove that something **must** happen you need to show that it happens always. So to show that dividing an irrational number ... |
How can I prove that dividing an irrational number by an irrational number (besides himself) **can** result in an integer? |
Start by assuming that you have a case where it *does* result in an integer, and see what that says about the irrational numbers. From there you should be able to give examples. That is, if $x/y = n$ for some integer $n$, what does that say about the relationship between $x$ and $y$? Choosing a specific integer $n$ ... |
1. The series for $\log (1+x)$ is convergent(by estimating radius of convergence) only with $|x| <1$. Then how is it still true for $x = 1$?
2. How is it still apparently true when $x$ is a roots of unity other than $-1$? Such as in the answers to this question: http://math.stackexchange.com/questions/11739
|
This is a follow up of http://math.stackexchange.com/questions/11587/upper-bound-binomial-sum
I was working on the problem in the above thread and noticed an interesting thing. I wanted to try and improve the bound Derek had (which was a quadratic in $n$).
If we reformulate the problem as Derek has (since for thi... |
It is a bit easier to understand the homology $H_1(X, \mathbb Z)$ for various compact surfaces in analogy with handles and so on. There seems to be a nice intuitive picture with handles, holes, etc to think of the first homology group, and similar heuristics for higher homology groups.
But almost all axiomatic treat... |
Sheaf cohomology is a well-studied topic with a lot of references available. For example Hartshorne's book. But for a certain paper I am reading now, I have to understand sheaf homology.
Could someone tell me some references? This is just sheaf homology in the topological sense; not in algebraic geometry.
|
Consider the power series ring in noncommutative associative formal variables $X, Y$ over the field $\mathbb C$. Let $P$ be a power series. Define the exponential $e^P$ and logarithm $\log (1+P)$ using the usual series expansions. The exponential maps from a neighborhood of $0$ to a neighborhood of $1$ and the logari... |
I was wondering about the generalization of the concept of convolution from the familiar one on real spaces and how many properties still remain.
For convolution on Lebesgue-integrable real-valued functions defined on a group equipped with measure, does each of the following properties holds? If not, what extra req... |
I was wondering about the generalization of the concept of convolution from the familiar one on real spaces and how many properties still remain.
For convolution on Lebesgue-integrable real-valued functions defined on a group equipped with measure, does each of the following properties holds? If not, what extra req... |
Let $M$ be a smooth manifold. Is it always possible to find a connected dense open subset $U$ of $M$ which is diffeomorphic to an open subset of **R**$^n$?
If we don't require $U$ to be connected, the answer is yes: it is enough to construct a countable collection of disjoint open "affines" whose union is dense, an... |
Do all manifolds have a densely defined chart? |
I was wondering about the generalization of the concept of convolution from the familiar one on real spaces and how many properties still remain.
For convolution on Lebesgue-integrable real-valued functions defined on a group equipped with measure, does each of the following properties holds? If not, what extra req... |
I'm trying to solve a differential equation problem that has to do with barometric pressure at a certain altitude.
The rate at which barometric pressure decreases with altitude is proportional to the pressure at that altitude. If the altitude in feet, then the constant of proportionality is 3.7 x 10<sup>5</sup>. The... |
I have a question about the set of functions from a set to another set. I am wondering about the degenerate cases. Suppose $X^Y$ denotes the set of functions from a set $Y$ to a set $X$, why is $|Y^{\emptyset}$|=1$ but $|\emptyset^Y|=0$ where $Y\neq \emptyset$? |
I have a question about the set of functions from a set to another set. I am wondering about the degenerate cases. Suppose $X^Y$ denotes the set of functions from a set $Y$ to a set $X$, why is $|Y^{\emptyset}|=1$ but $|\emptyset^Y|=0$ where $Y\neq \emptyset$? |
The definition of $A^B$ is "the set of all functions with domain $B$ and codomain $A$".
A function $f$ from $B$ to $A$ is a set of ordered pairs such that:
1. If $(x,y)\in f$, then $x\in B$ and $y\in A$.
2. For every $b\in B$ there exists $a\in A$ such that $(b,a)\in f$.
3. If $(b,a)$ and $(b,a')$ are in... |
I'm assuming that $G/H$ represents the left cosets of $H$ in $G$, that is the sets of the form $gH$ with $g\in G$, with the action of $G$ on $X$ being given by $x\cdot(gH) = xgH$ (left multiplication), and that $X^K$ is the set of fixed points of $K$; that is, all $gH\in X$ such that for all $k\in K$, $k(gH)=gH$.
If... |
The definition of $A^B$ is "the set of all functions with domain $B$ and codomain $A$".
A function $f$ from $B$ to $A$ is a set of ordered pairs such that:
1. If $(x,y)\in f$, then $x\in B$ and $y\in A$.
2. For every $b\in B$ there exists $a\in A$ such that $(b,a)\in f$.
3. If $(b,a)$ and $(b,a')$ are in... |
Let $M$ be a smooth connected manifold. Is it always possible to find a connected dense open subset $U$ of $M$ which is diffeomorphic to an open subset of **R**$^n$?
If we don't require $U$ to be connected, the answer is yes: it is enough to construct a countable collection of disjoint open "affines" whose union is... |
The first thing you have to understand is that notes are not uniquely defined. Everything depends on what tuning you use. I'll assume we're talking about <a href="http://en.wikipedia.org/wiki/Equal_temperament">equal temperament</a> here. In equal temperament, a half-step is the same as a frequency ratio of $\sqrt[1... |
The first thing you have to understand is that notes are not uniquely defined. Everything depends on what tuning you use. I'll assume we're talking about <a href="http://en.wikipedia.org/wiki/Equal_temperament">equal temperament</a> here. In equal temperament, a half-step is the same as a frequency ratio of $\sqrt[1... |
Depending on what you consider a manifold, the <a href="http://en.wikipedia.org/wiki/Long_line_%28topology%29">long line</a> may be a counterexample.
And for a non-connected manifold, surely the answer is no? Take your favorite smooth manifold, and take a disjoint union of more than $\mathfrak{c}$ copies of it. Ag... |
The first thing you have to understand is that notes are not uniquely defined. Everything depends on what tuning you use. I'll assume we're talking about <a href="http://en.wikipedia.org/wiki/Equal_temperament">equal temperament</a> here. In equal temperament, a half-step is the same as a frequency ratio of $\sqrt[1... |
I have the following problem. There is a binary relation $\succeq$ defined on a separable metric space $X$, and $\succeq$ is total, transitive, and closed (as a subset of $X\times X$, in the product metric). There exists a set $Y\subseteq X$ that bounds the elements of $X$ in order (that is, for each $x \in X$ one can ... |
Let $\{r_1, r_2, r_3,\ldots \}$ be an enumeration of the rationals in $[0,1]$, and let $(a_k)$ be a sequence such that $\sum_{k=1}^{\infty}{a_k}$ converges absolutely. Set $f_k(x) = a_k\,|x-r_k|^{-1/2}$. I'd like to show that $$\sum_{k=1}^{\infty}{\int_{[0,1]}{|f_k(x)|\,dx}}<\infty\,.$$
I've rewritten the sum as $$\... |
So I am studying for my calculus midterm and I had the following question:
If $f_{x}(a, b)$ and $f_{y}(a,b)$ both exist then $f$ is differentiable at $(a,b)$
I answered true, but the answer is false. Why is that? I havn't done real analysis yet (dropped it this term) so I won't know what your talking about if it... |
Think about when can you say a function is differentiable?
Remember that $f_x$ and $f_y$ gives you the partial derivatives in just 2 directions namely $X$ axis and $Y$ axis respectively. |
Factoring a rational function as:
$$\frac{(x-a)(x-b)\cdots(x-z)}{(x-A)(x-B)\cdots(x-Z)}$$
Clearly displays the x-intercepts (roots) and vertical asymptotes (poles) of a rational function.
Similarly, dividing the denominator D into the numerator N to get N = DQ+R and writing N/D as Q + R/D clearly displays the ... |
Can elliptic curve (defined as part of an ellipse, with extent not bigger than 90 degrees) be represented by quadratic Bezier curve? |
Can elliptic curve be represented by quadratic Bezier curve? |
Why is it that cubics are separable over fields that are not of characteristic $2$ or $3$?
This is the starting point for some a discussion of the Galois group of a cubic, but I seem to be stuck right off the bat. |
Can elliptic arc (defined as part of an ellipse, with extent not bigger than 90 degrees) be represented by quadratic Bezier curve? |
Can elliptic arc be represented by quadratic Bezier curve? |
I was wondering about the generalization of the concept of convolution from the familiar one on real spaces and how many properties still remain.
For convolution on Lebesgue-integrable real-valued functions defined on a group equipped with measure, does each of the following properties holds? If not, what extra req... |
So I am studying for my calculus midterm and I had the following question:
If $f_{x}(a, b)$ and $f_{y}(a,b)$ both exist then $f$ is differentiable at $(a,b)$
I answered true, but the answer is false. Why is that? I haven't done real analysis yet (dropped it this term) so I won't know what your talking about if i... |
There's a lot of similar things that are called "trees" in graph theory. I interpret this question to mean full binary trees (see [Wikipedia][1]) -- that is, each non-leaf node has a "left" and a "right" descendant.
*Hint*: How can you modify a full binary tree with n+1 nodes to a full binary tree with n nodes? W... |
How do you define a leaf? The idea of structural induction would be to show that whenever you add a new node to an existing tree, the difference between leaves and nodes without right siblings stays constant. Without the leaf definition I can't help further. |
[Elementary Theory of Numbers](http://books.google.com/books?id=ktCZ2MvgN3MC&printsec=frontcover&dq=sierpinski&hl=en&ei=e_rtTK2HNcSAlAeC1rWtDA&sa=X&oi=book_result&ct=result&resnum=1&ved=0CCMQ6AEwAA#v=onepage&q=sierpinski&f=false) by Sierpinski. |
I was trying to solve this congruence equation: $2ax+b\equiv 0$ mod $5$. Here, $b$ is any integer and $a$ is an integer not divisible by $5$. Does a solution always exist? I don't understand why they have set the condition above on $a$. As should be clear from my other question on elementary number theory, I am not ver... |
Question: Let $U$ denote a subset of $\mathbb{R}$. We say that $U$ is an open set when for every $x \in U$ there is an $\epsilon > 0$ for which $U_{\epsilon}(x) = (x - \epsilon, x +\epsilon)$ is contained in $U$. Show:
(i) For $a,b \in \mathbb{R}$ the interval $(a,b)$ is open, but the interval $[a,b]$ is not.
(ii... |
This question arises from a Fourier transform class I took about a year back.
The poisson summation formula is:
$\displaystyle \sum_{n= - \infty}^{\infty} f(n) = \displaystyle \sum_{k= - \infty}^{\infty} \hat{f}(k)$.
where $\hat{f}$ is the Fourier Transform of $f(x)$.
It is interesting since this is true fo... |
I was trying to solve this congruence equation: $2ax+b\equiv 0 \pmod 5$. Here, $b$ is any integer and $a$ is an integer not divisible by $5$. Does a solution always exist? I don't understand why they have set the condition above on $a$. As should be clear from my other question on elementary number theory, I am not ver... |
Intuitively, a set $U$ is open if every point in the set can be completely surrounded by points that are all in the set; here, "surrounded" means that an entire little interval centered at $x$ is completely contained in $U$, which means, in a sense, that $x$ is *really* inside $U$. A set is open if every point in the s... |
Question: Let $U$ denote a subset of $\mathbb{R}$. We say that $U$ is an open set when for every $x \in U$ there is an $\epsilon > 0$ for which $U_{\epsilon}(x) = (x - \epsilon, x +\epsilon)$ is contained in $U$. Show:
(i) For $a,b \in \mathbb{R}$ the interval $(a,b)$ is open, but the interval $[a,b]$ is not.
(ii... |
Perhaps you've come across the following theorem in your studies?
> If $gcd(a,m)=1$, then there is an $x$ such that $ax\equiv 1\pmod{m}$, and any two such $x$ are congruent $\pmod{m}$. If $gcd(a,m)>1$, then there is no such $x$.
Essentially, this means an integer $a$ has a multiplicative inverse modulo $m$ if and... |
Question: Let $U$ denote a subset of $\mathbb{R}$. We say that $U$ is an open set when for every $x \in U$ there is an $\epsilon > 0$ for which $U_{\epsilon}(x) = (x - \epsilon, x +\epsilon)$ is contained in $U$. Show:
(i) For $a,b \in \mathbb{R}$ the interval $(a,b)$ is open, but the interval $[a,b]$ is not.
(ii... |
In the situation of having a high entropy random number generator, that generates numbers in the range of 0 and 2,147,000,000.
If i have a list of 1,000,000 integer values, what are the chances that a random number will already be on my list? |
This question arises from a Fourier transform class I took about a year back.
The poisson summation formula is:
$$\displaystyle \sum_{n= - \infty}^{\infty} f(n) = \displaystyle \sum_{k= - \infty}^{\infty} \hat{f}(k)$$.
where $\hat{f}$ is the Fourier Transform of $f(x)$.
It is interesting since this is true ... |
This question arises from a Fourier transform class I took about a year back.
The poisson summation formula is:
$$\displaystyle \sum_{n= - \infty}^{\infty} f(n) = \displaystyle \sum_{k= - \infty}^{\infty} \hat{f}(k)$$
where $\hat{f}$ is the Fourier Transform of $f(x)$.
It is interesting since this is true f... |
For a common basis, I'll state basic definitions of a category and the relation type I'm thinking of. They're here for quick clarity, not precision, so feel free to revise for an answer.
Category:
A collection of objects, a collection of arrows each with a source and target among said objects, identity arrows, an... |
What is the difference between Categories and Relations? |
Is the essential difference between one-variable calculus and multi-variable calculus exterior differential or something else? |
What is the essential difference between one-variable calculus and multi-variable calculus? |
There's essentially no difference in the *concept* of the derivative. It is still the best linear approximation to your function at each point. I.e. $f$ differentiable at $x_0$ still means that
$$ f(x_0+h) = f(x_0) + f'(x_0)x_0 + \varphi(h), $$
for $h$ in some nbhd. of $0$ and $\varphi$ a continuous function that ten... |
Lets imagine that we play rock-paper-scissors game. Opponent shows rock, paper and scissors with probabilities of Pr, Pp and Ps, respectively. Pr + Pp + Ps = 1. This distribution is time-dependent (because opponent may change his strategy on the basis of our and his previous actions). I wand to predict this distributio... |
> Do you think it is possible to
> successfully study mathematics with
> such a short initial knowledge and not
> having my full day to do it?
That depends on your university course and how faster you can learn and get skills, but you will like to devote at least 4-5 hours day, and will want to do as much exercis... |
I am learning about discrete probability distributions and found 2 definitions for Geometric Distributions from [wikipedia][1]:
1. The probability distribution of the number X of Bernoulli trials needed to get one success, supported on the set { 1, 2, 3, ...}
2. The probability distribution of the number Y = X − 1 of... |
Which geometric distribution to use? |
Qiaochu is right: categories are much more general. Let me provide a concrete example which, while in a sense trivial, may illustrate just how much more you could get from a category than you can from a reflexive and *transitive* relation.
Consider the positive integers $\mathbb P$. The usual total order $\leqslant$... |
Qiaochu is right: categories are much more general. Let me provide a concrete example which, while in a sense trivial, may illustrate just how much more you could get from a category than you can from a reflexive and *transitive* relation.
Consider the positive integers $\mathbb P$. The usual total order $\leqslant$... |
I think the cone (or what is also called the "half cone") is a differential manifold but not a smooth manifold.
Can anyone help me understand this the nuts and bolts way?
How explicitly can I write down the differential structure on the cone?
Also what is the natural metric on it?
(Is that what is called... |
I have seen this claim on Wikipedia and other places. Which branch of mathematics does this result come from? |
Why can't erf be expressed in terms of elementary functions? |
Let $A$ be the infinitesimal generator of a $C_0$-semigroup $(S(t))_{t \geq 0}$. Now, for every $x_0 \in X$ the map $t \mapsto S(t) x_0$ is a mild solution of
\begin{equation}\label{eq:1}
\dot{x} = Ax, \quad x(0) = x_0. \qquad \text{(*)}
\end{equation}
Now, a continuous function $x: [0, \infty) \to X$ is called... |
[Omar Khayyam][1] is known his for significant progress in solving cubic polynomial equations. For example, his biography on [www-history.mcs.st-andrews.ac.uk][2] says
> (...) This problem in turn led Khayyam to
> solve the cubic equation x^3 + 200x =
> 20x^2 + 2000 and he found a positive
> root of this cubic by... |
[Omar Khayyam][1] is known for his significant progress in solving cubic polynomial equations. For example, his biography on [www-history.mcs.st-andrews.ac.uk][2] says
> (...) This problem in turn led Khayyam to
> solve the cubic equation x^3 + 200x =
> 20x^2 + 2000 and he found a positive
> root of this cubic by... |
[Omar Khayyam][1] is known for his significant progress in solving cubic polynomial equations. For example, his biography on [www-history.mcs.st-andrews.ac.uk][2] says
> (...) This problem in turn led Khayyam to
> solve the cubic equation x^3 + 200x =
> 20x^2 + 2000 and he found a positive
> root of this cubic by... |
Intuitively, a set $U$ is open if every point in the set can be completely surrounded by points that are all in the set; here, "surrounded" means that an entire little interval centered at $x$ is completely contained in $U$, which means, in a sense, that $x$ is *really* inside $U$. A set is open if every point in the s... |
Here is a reference -first result in google:
http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.ijm/1256060422
The author (who now works in a bank) needs his construction of sheaf homology to prove a criterion for the vanishing of certain integrals of differential forms, though the pap... |
Intuitively, a set $U$ is open if every point in the set can be completely surrounded by points that are all in the set; here, "surrounded" means that an entire little interval centered at $x$ is completely contained in $U$, which means, in a sense, that $x$ is *really* inside $U$. A set is open if every point in the s... |
Given $N$ random iid variables, $X_1, \ldots, X_N$, with a uniform probability distribution $\in [0, 1)$ what is the distribution of $max_{i = 1 \ldots N}(X_i)$? |
Will every n-th root of 2 always be an irrational number? If yes, how can I prove that?
|
Is n-th root of 2 an irrational number? |
What does this expression means? |
When we consider the Taylor Series expansion of $f(x)=b^x$ for some $b \in \mathbb{R}$, we see that $$b^x = 1 + \sum_{n=1}^{\infty}\frac{(log(b))^n}{n!}x^n$$. We can substitute $x$ for $b^x$ to find that $$ b^{b^{x}} = 1 + \sum_{n=1}^{\infty}\frac{(log(b))^n}{n!}b^{xn}$$.
Now, let's say that we want to find a funct... |
Can the following expansion series be iterated a real amount of times? |
What does this expression mean?
$$f\in C^2[a,b]$$ |
When we consider the Taylor Series expansion of $f(x)=b^x$ for some $b \in \mathbb{R}$, we see that $$b^x = 1 + \sum_{n=1}^{\infty}\frac{(\log(b))^n}{n!}x^n.$$ We can substitute $x$ for $b^x$ to find that $$ b^{b^{x}} = 1 + \sum_{n=1}^{\infty}\frac{(\log(b))^n}{n!}b^{xn}.$$
Now, let's say that we want to find a fun... |
When we consider the Taylor Series expansion of $f(x)=b^x$ for some $b \in \mathbb{R}$, we see that $$b^x = 1 + \sum_{n=1}^{\infty}\frac{(\log(b))^n}{n!}x^n.$$ We can substitute $x$ for $b^x$ to find that $$ b^{b^{x}} = 1 + \sum_{n=1}^{\infty}\frac{(\log(b))^n}{n!}b^{xn}.$$
Now, let's say that we want to find a fun... |
> **Possible Duplicate:**
> [Number theory proving question?](http://math.stackexchange.com/questions/7473/number-theory-proving-question)
<!-- End of automatically inserted text -->
Dear friends,
Since b, x, y, z, ... integers greater than 1, how can we prove that
gcd (b ^ x - 1, b ^ y - 1, b ^ z - 1 ,...... |
Prove that $\lim_{x \to 2} \frac{x^{2}-2x+9}{x+1}$ using an epsilon delta proof.
So I have most of the work done. I choose $\Delta = min{\frac{1}{2}, y}$
$f(x)$ factors out to $\frac{|x-3||x-2|}{|x+1|}$
But $|x-3| < \frac{3}{2}$ for $\delta = \frac{1}{2}$ and also $|x+1| > 5/2$ (I'll spare you the details). ... |
Prove that $\lim\limits_{x \to 2} \frac{x^{2}-2x+9}{x+1}$ using an epsilon delta proof.
So I have most of the work done. I choose $\delta = min{\frac{1}{2}, y}$,
$f(x)$ factors out to $\frac{|x-3||x-2|}{|x+1|}$
But $|x-3| \lt \frac{3}{2}$ for $\delta = \frac{1}{2}$ and also $|x+1| > 5/2$ (I'll spare you the d... |
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