# Tagged Questions

Homework questions are welcome as long as they are asked honestly, explain the problem, and show sufficient effort. Please do not use this as the only tag for a question. For the answers on homework questions, helpful hints or instructions are preferred to a complete solution. Please do not add ...

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### Taylor Expension for F' centered at infinity

i have a question Write Taylor expension for F' centered at infinity. This series will converge uniformly for /z/>R, R Large.
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### Step-by-step proof of principal ideals.

Could someone go through a step-by-step proof of: Let $\theta:R\to S$. Show that if every ideal of $R$ is principal, than every ideal of $S$ is also principal. I really just have the ...
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### How can I answer the question

On Monday, it took Helen 3 hours to do a page of science homework exercises. The next day she did the same number of exercises in 2 hours. If her average rate on Monday was p exercises per hour, what ...
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### Solving a weird recurrence relation using exponential generating functions and differential equations

So the recurrence relation is: $a(n) = (n-1)\cdot a(n-2) + (n-1)(n-2)\cdot a(n-3)$ I've tried several things, but the instructions are to use a differential equation and nothing I'm doing seems to ...
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### If $a+b+c \ge 1$ and $a,b,c>0$, prove that $\frac{1}{2a+s}+\frac{1}{2b+s}+\frac{1}{2c+s} \ge \frac{1}{s}$, where $s=ab+bc+ca$.

What I know is that $$s \le \frac{(a+b+c)^2}{3} \ge \frac{1}{3}$$But as you can see the sign is pointing to different sides. So I can't see how this could be helpful. Just a small observation. I don't ...
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### Newton's Method; Numerical Analysis [on hold]

How can newton's method be used to solve $$\int_{0}^{x} e^{-t^2} dt = 1/3. ?$$
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### Laurent Series Difficulty

Hello all at StackExchange, I'm having some trouble understanding computing the Laurent series for different domains. Here's my approach to finding the Laurent series for $\dfrac{3}{(z+1)(z-2)}$ for ...
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### First $3$ non-zero terms of the Maclaurin Series $\frac{1}{\sqrt{4+x^3}}$

Since each derivative will be multiplied by $3x^2$, are all the terms of this Maclaurin series $0$?
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### Exponential and power functions through two points

I have a problem where I'm asked to determine the constants of exponential and power functions that go through both points (5, 50) and (10, 1600). I have tried to solve them below, but would ...
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### Find $\sum_{k=0}^{n}2^ks(n,k)$, where $s(n,k)$ is the Stirling number of the first kind?

Find $\sum_{k=0}^{n}2^ks(n,k)$, where $s(n,k)$ is the Stirling number of the first kind? I was able to find that $\sum_{k=0}^{n}x^kc(n,k)=\dfrac{(n-1+x)!}{(x-1)!}$ where $c(n,k)$ is the signless ...
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### Prove that $(a^2+b^2)(b^2+c^2)(c^2+a^2) \geq 8a^2b^2c^2$

This is my proof. I'm not sure if it is true but perhaps someone would tell me yes or (no and why). Since $(a^2+b^2), (b^2+c^2), (c^2+a^2)$ are greater than or equal to zero, then ...
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### What are a and b?

$a$ and $b$ are two positive integers. If $ab=1260$, $gcd(a,b)=3$, and when $a$ is divided by $b$ the remainder is 18, what are $a$ and $b$? How do you solve this? EDIT It looks like an ...
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### 1000 Doors Homework Problem [duplicate]

I am faced with the following problem as homework- a man has 1000 doors. he opens every door, and then he closes every second door. Then he works on every third door- if it's open, then he closes it. ...
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### It's a logarithmic worksheet and O can't solve it.

$\log_ax=p$, $\log_bx=q$ , $\log_{abc}x$=r. What is $\log_cx$?.. It's on my math homework can someone solve it cause I need it.
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### How many students need to be checked to be 90% sure they got a grade of 70..80?

Can you help me on some question i'm stuck on? Let X be a random variable of the average grade of the students in some course. E[X] = 75 ...
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### Characteristic function of an integer-valued distribution, inversion formula

I am working on the following: Show that if $\varphi$ the characteristic function of an integer-valued distribution then \begin{align*} \mathbb P(X = k) = \frac{1}{2\pi} \int_{-\pi}^\pi e^{-itk} ...
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### When is the set statement: (A\B)⊕(A ∩ B) = A true?

"When is the set statement: (A\B)⊕(A ∩ B) = A true? Is it sometimes true, never true, or always true? If sometimes, state the specific cases where it is. A & B are arbitrarily selected ...
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### Proof of solid angle theorem

I have a homework problem to prove about the solid angle. The book says: Let S be a smooth parametric surface and let P be a point such that each line that starts at P intersects S at most once. ...
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### How to work out this easy fraction?

I need help working out this fraction, I know it seems quite easy but I'm a bit stuck. The question is: $$\frac{5/2}{5/9}$$ My attempt was changing the denominators by multiplying by $2$ to make ...
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### Permutation and combination.

In how many ways can 12 indistinguishable apples and 1 orange be distributed among 3 distinguishable children in such a way that each child gets at least one fruit? What if the apples are different ...
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### What's the probability that more than 10 students will get their hw back?

This question is confusing me... Students submitted their homework and now they will get them back randomly. What can you say about the probability that more than 10 of them will get their own ...
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### Finding the Riemann stieltjes integral using partitions

Please take a look at the following example : $α(x)=x$ when $0≤x≤1$ $α(x)=x+2$ when $1< x≤2$ Evaluate $\int_{0}^{2}xdα(x)$ I solved this using the integration by parts formula and got the ...
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### conditional expectation of squared standard normal

Let $A,B$ independent standard normals. What is $E(A^2|A+B)$? Is the following ok? $A,B$ iid and hence $(A^2,A+B),(B^2,A+B)$ iid. Therefore we have $\int_M A^2 dP = \int_M B^2 dP$ for every ...
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### Verify that $\bigl(p\to(q\to r)\bigr)\to \bigl((p\to q)\to (p\to r)\bigr)$ is a tautology.

Verify that $\bigl(p\to(q\to r)\bigr)\to \bigl((p\to q)\to (p\to r)\bigr)$ is a tautology. I am confused on this whole tautology even after looking at examples both in my book and on-line. I ...
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### Show that $\dfrac{\mathbb Z[x]}{(2,x)}$ is a field.

Show that $\dfrac{\mathbb Z[x]}{(2,x)}$ is a field, where $$(2,x)=\{p(x)\in\mathbb Z[x]:\text{the constant term of p(x) is even}\}$$ Thus $\dfrac{\mathbb Z[x]}{(2,x)}=\{(2,x),1+(2,x)\}.$ Since ...
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### Check my short proof - asymptotic approximation, which function is bigger

The goal of this exercise is to show that $\ln(n+1)-\ln(n) = O(\frac{1}{n})$ what I did is: I used the fact that if $f=O(g)$ then $\frac{f}{g}=O(1)$. $\ln(n+1)-\ln(n)=\ln(\frac{n+1}{n}) = \ln(O(1))$ ...
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### Problem finding limit - which function is asymptotically larger

I have a homework question, so please don't answer fully but I would appreciate a push in the right direction. Basically we need to figure out if $n^{n+\frac{1}{2}}e^{-n}$ is larger,smaller, or equal ...
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### Proving $U_\epsilon = \{x \in M | d(x, C) < \epsilon\}$ is open, given that $C$ is non-empty

In a metric space $(M, d)$ let $C \subset M$ and non-empty. Given $\epsilon > 0$ we define: $$U_\epsilon = \{x \in M | d(x, C) < \epsilon\}$$ Prove $U_\epsilon$ is open. I am ...
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### If $a,b,c>0$ and $a+b+c=1$, prove that $\sqrt{\frac{ab}{c+ab}}+\sqrt{\frac{bc}{a+bc}}+\sqrt{\frac{ac}{b+ac}} \le \frac{3}{2}$.

I can't see any ways I could use the fact that $a+b+c=1$. I've tried solving the inequality using various AM-GM inequalities, but I just can't make it. I need some help. Thanks.
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### I need to prove that $\mathbb{C}/\mathbb{R}\cong \mathbb{R}$
I need to prove that $\mathbb{C}/\mathbb{R}\cong \mathbb{R}$, by the this theorem: $G/\ker(\varphi)\cong Im(\varphi)$. I tried to find $\varphi$ that will give me this but I didn't succeed. Maybe ...
### For which values ​​of $z$ the inequality $|e^{z-1}|<2$ holds
I want to find for which values of $z$ the following inquality holds $$|e^{z-1}|<2$$ what I tried to do is: $$|e^{z-1}|=|e^{x-1+y\mathbb{i}}|<2$$ $$=e^{x-1}\cdot(\cos(y) + \mathbb{i} \sin(y))$$ ...