# All Questions

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### How can I prove that it is an Entire Function

Prove that if $$f(z)=\left\{ \begin{array}{ll} \frac{\cos z}{z^2-(\pi /2)^2} & \hbox{when} \; z\neq \mp \pi/2\\ -\frac{1}{\pi}, & \hbox{when} \;z= \pi/2. \end{array} \right.$$ ...
19 views

### Proof about composed functions (elementary number theory)

Let f : X → Y and g : Y → X be functions and assume $g ◦ f = I_X$. Prove of g is injective then $f ◦ g = I_Y$. Approach if g is the left inverse of f then there exists $x\in X$ and $y \in Y$ such ...
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### Find Unique Index for a Subset S

I'm looking for a way to assign a unique number to a particular subset of S. S is a set of n distinct integers from 1 through n. Now, take the set of all subsets of length k where order doesn't ...
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### Challanging problems on [Grade-12]Complex Number [on hold]

recently we are introduced to interesting world of complex number but except for 3-5 problems in the my books,all the problems are just plug-and chug,expression manipulation,etc.. which bores me out ...
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### There are 40 available time slots for examinations. You need to schedule the A and B exams according to the following rules:

NOTE: This is homework so would appreciate if I could get some explanations instead of just straight answers. Really struggling with this question and to be honest, don't really know where to even ...
19 views

### counting the forecasts of 20 chess games

I have a Question... The results of 20 chess games (win, lose, draw) have to be predicted. How many different forecasts can contain exactly 15 correct results? I don't really understand this ...
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### How to interpret multi-conditional piecewise functions.

I'm trying to simulate hysteresis and the its inverse for a control problem. This is a model found in [Tao & Kokotovic, Adaptive Control Systems with Actuator and Sensor Nonlinearities] to ...
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### Why we can not get a Plucker mapping under the Supergrassmannian?

Given a grassmannian, we can obtain a Plucker mapping. Reading the book "Gauge Field Theory and Complex Geometry", I know that we can not get a Plucker mapping under the supergrassmannian generally. ...
16 views

### Taylor series integration

I am having trouble with the following question: Integrate the Taylor series $$e^{(-t^2)} = \sum^\infty_{n=0} \frac{(-t^2)^n}{n!}$$ term-by-term to obtain the Taylor series for erf (error function) ...
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### Prove $-\frac{\ln(1-x^2)}{1-x^2}=H_1x^2+H_2x^4+H_3x^6+H_4x^8+\cdots$

$H_n$ is nth the harmonic numbers $x<1$ (1) $$-\frac{\ln(1-x^2)}{1-x^2}=H_1x^2+H_2x^4+H_3x^6+H_4x^8+\cdots$$ A different approach of representing $\ln(x)$ let expand out the series ...
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### An analytic method to prove a specific curve is closed

In my study of Hamiltonian dynamics I have come across a Hamiltonian dynamic system with a solution curve I know to be closed via computer and via intuition but I require a rigorous way to prove this, ...
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### What is the solution for the Logarithmic CompSci question? [on hold]

Facts: My alphabet contains m digits. Each digit is represented in memory by 1 byte. A word is any string of digits. Words are separated by a single non-alphabetic character. It is represented in ...
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### General Solution by complexification $\,y''-3y' =2e^{t}\sin 2t$

General Solution by complexification $\,y''-3y' =2e^{t}\sin 2t$ I could use some help here as I don't know what complexification is and I tried googling it but the material was sort of confusing. ...
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### There are $101$ positive integers that sum to $300$. Can we find a subset of these integers that sums to $100$? [duplicate]

We are given a set of $101$ positive integers that sum to $300$. Since summation of $101$ distinct numbers cannot be $300$, repetition among the $101$ positive integers exists. Can we choose a group ...
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### How to find area of isosceles triangle when given two heights? [on hold]

So I know the sine and cosine theorem and I tried using them but I got nowhere. (I got to an equation which I can't solve and I know there must be an easier method since we have not studied how to ...
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### Proving that largest root (obtained via P.C.A.) is a symmetric function

Suppose, we are given $\textbf{X} = (X_1, X_2, \ldots,X_m)$ and $\textbf{Y} = (Y_1, Y_2, \ldots, Y_n)$. Also, we are given, S = pooled variance. If we implement Principal Component Analysis (P.C.A.) ...
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### Goldberg compound probability problem- guess the correct colour ball from an urn

I am working my way through an example problem from Goldberg's "Probability: An Introduction". There are x red balls and x green balls in an urn. Total number of balls in the urn is 5. You must guess ...
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### Find Surface Area Via a Line Integral (Stokes' Theorem)

I am trying to use Stokes' Theorem to calculate the surface area of a parametrized surface via a line integral. The surface is the part of $z= x^2+y^2$ below the plane $z=5$. I know this can be done ...
23 views

### build absolute value equations know solution

We have absolute value equations with unknown coefficients: $$|x + a| = b$$ and we know the solutions: $$x = 11 \text{ and } x = 5$$ We need to find $a$ and $b$. From $$11 + a = b \\ 5 + a = -b$$ we ...