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Microeconomics (quasi-linear utility function)
Suppose that Sally’s preferences over baskets containing food (good x), and clothing (good y), are described by the utility function $U(x,y)=\sqrt{x}+y$. ...
Apr 18, 2026
Archive: News
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The Eigenvalues of a block matrix
It is known that all $B$, $C$ and $D$ are $3 \times 3$ matrices. And the eigenvalues of $B$ are $1, 2, 3$; $C$ are $4, 5, 6$; and $D$ are $7, 8, 9$. What ...
Apr 18, 2026
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How do we calculate the area of a region bounded by four different curves?
Calculate the area(express both respectively in integral with one variable) bounded by the following curves (i.e. the shape with one side corresponding to...
Apr 18, 2026
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Does $\mathbb{F}_9$ contain a 4th root of unity?
I realised that I don't know how to construct $\mathbb{F}_9$. I'm guessing that $\mathbb{F}_9 = \mathbb{F_3(\theta)}$, where $\theta$ is the roo...
Apr 18, 2026
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summable sequence
I am looking for a sequence $\beta_n\in(0,1)$ such that (i) $~ \prod_{n\in\mathbb N} \beta_n =0$, (ii) $~\sum_{n\in\mathbb N} (1-\beta_n)< +\infty$. Do...
Apr 18, 2026
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Compute the gradient of mean square error
Let $Y = \begin{pmatrix} y_1 \\ \cdots \\ y_N\end{pmatrix}$ and $X = \begin{pmatrix} x_{11} & \cdots & x_{1D} \\ \cdots & \cdots & \cdots ...
Apr 17, 2026
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Numerical Differentiation Matlab
I am trying to estimate the second derivative of $\sin(x)$ at $0.4$ for $h=10^{-k}, \ \ k=1, 2, ..., 20$ using: $$\frac{f(x+h)-2f(x)+f(x-h)}{h^2}\tag{1}$$...
Apr 17, 2026
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Integrating exponent with polynomial
http://i.stack.imgur.com/4tXNr.jpg $e^{x^2/2}\int e^{-x^2/2}(-x^3+x)\ dx$ turns out to be equal to $e^{x^2/2}[e^{-x^2/2}(x^2+1)] $ Is there a easier metho...
Apr 17, 2026
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What are "tan" and "atan"?
As the title says, I'm confused on what tan and atan are. I'm writing a program in Java and I came across these two mathematical functions. I kn...
Apr 17, 2026
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Equation of latus rectum of parabola
If parabola $\left ( y+1 \right )^{2}=k\left ( x-2 \right )$ passes through a point (1,-2), then equation of its latus rectum and directrix ? My attempt I...
Apr 17, 2026
