Replace the clichés in boldface type with more original Ianguage.

All we need to do is wrap it up. (take care of some final details)

When invading Persia, Alexander the Great followed which example of Cyrus the Great?

In this problem we explore some of the more useful theorems (stated without proof) involving Hermite polynomials. (a) The Rodrigues formula says that $H_{n}(\xi)=(-1)^{n} e^{\xi^{2}}\left(\frac{d}{d \xi}\right)^{n} e^{-\xi^{2}}$. Use it to derive $H_{3}$ and $H_{4}$. (b) The following recursion relation gives you $H_{n+1}$ in terms of the two preceding Hermite polynomials: $H_{n+1}(\xi)=2 \xi H_{n}(\xi)-2 n H_{n-1}(\xi)$. Use it, together with your answer in (a), to obtain $H_{5}$ and $H_{6}$. (c) If you differentiate an nth-order polynomial, you get a polynomial of order (n-1). For the Hermite polynomials, in fact, $\frac{d H_{n}}{d \xi}=2 n H_{n-1}(\xi)$. Check this, by differentiating $H_{5}$ and $H_{6}$. (d) $H_{n}(\xi)$ is the nth z-derivative, at z=0, of the generating function $\exp \left(-z^{2}+2 z \xi\right)$; or, to put it another way, it is the coefficient of $z^{n} / n !$ in the Taylor series expansion for this function: $e^{-z^{2}+2 z \xi}=\sum_{n=0}^{\infty} \frac{z^{n}}{n !} H_{n}(\xi)$. Use this to obtain $H_{1}$, $H_{2}$, and $H_{3}$.

Fill in the blanks

The graph of a quadratic function is symmetric about its ________.

The equations of parabolas, circles, and ellipses are given. Graph the equation.

$$72 x^2=144 y$$

Complete the following conversation with the por where necessary. If por is not required, mark the blank with an X. The first one has been done for you.

PABLO: Creo que las chuletas se cocinan________unos veinte minutos.

It is necessary to make a statement about the presence of right triangles when you use the Right Triangle Congruence Theorems. If you have previously identified the right angles, the reason is the definition of right triangles.

Create a proof of the following.

Given: $\overline{G U}$ is the $\perp$ bisector of $\overline{D B}$

Prove: $\triangle G U D \cong \triangle G U B$

Find the smallest relation containing the relation {(1, 2), (1, 4), (3, 3), (4, 1)} that is a) reflexive and transitive. b) symmetric and transitive. c) reflexive, symmetric, and transitive.

Why might the lines break where they do, and how does the poem’s shape contribute to its meaning? Why do you think Clifton uses no capital letters in the poem?

Classify each of the following statements as either true or false. When solving a system of two equations algebraically leads to an equation that is always true, the system has an infinite number of solutions.

For this question, refer to the Condo Care Company situation and the graph of $t=\frac{48}{w}$.

Why is the domain discrete?

Calculate each of the following integrals or say why it cannot be done with the methods and theorems in this book. Let $\vec{F} = x^3\vec{i} + y^3\vec{j} + z^3\vec{k}$.

$\int_W \vec{F} \cdot (\vec{i} + \vec{j} + \vec{k})dV$ where $W$ is the box $0 \leq x \leq 1, 0 \leq y \leq 2, 0 \leq z \leq 3$.

¿Cuál de las siguientes situaciones se produjo tras la caída del muro de Berlín?

$A$. Europa siguió dividida entre líneas ideológicas.

$B$. La Unión Europea se derrumbó.

$C$. Todas las naciones europeas se convirtieron en miembros de la OTAN.

$D$. Gran parte de Europa formó un mercado económico único.

If the input to the $RLC$ circuit of the given figure is $v \mathrm{~s}(t)=$ $u(t):$ (a) Find the output voltage transform across each element. (b) Compare the three outputs with regards to their respective poles and zeros. (c) Use the initial and final value theorems to determine the value of the voltage across each element at $t=0$ and $t=\infty$. What conclusions can one draw regarding the results?