A positive number

$$\epsilon$$

and the limit L of a function f at

$$+ \infty$$

are given. Find a positive number N such that |f(x)-L|<

$$\epsilon$$

if x>N.

$$\lim _ { x \rightarrow + \infty } \frac { 4 x - 1 } { 2 x + 5 } = 2 ; \epsilon = 0.1$$

The designations 1A through 8A used for certain families of the periodic table are helpful for predicting the charges on ions in binary ionic compounds. In these compounds, the metals generally take on a positive charge equal to the family number, and the nonmetals take on a negative charge equal to the family number minus 8. Thus the compound formed from sodium and chlorine contains $\mathrm { Na } ^ { + }$ and $\mathrm { Cl } ^ { - }$ ions and has the formula $\mathrm { NaCl } .$ Predict the formula and the name of the binary compound formed from the following pairs of elements. Rb and F

Exhibit all Sylow 3-subgroups of $SL_2(\mathbb{F}_3)$.

Simplify the expression. Write your answer using only positive exponents.

$$\left( \frac { 2 } { 3 } \right) ^ { 4 }$$

Tell which number is greater. 15. 80%, 7/9

$$\begin{array}{l} \text { Find } d y / d x \text { by implicit differentiation. } \end{array}$$

$$\sqrt { x + y } = x$$

sketch the curve represented by the parametric equations (indicate the orientation of the curve) x = 4 cos θ , y = 2 sin θ

If relativistic effects are to be less than 1$\%$, then $\gamma$ must be less than 1.01. At what relative velocity is $\gamma$ = 1.01?

Of the functions $\Delta H ^ { \circ } , \Delta S ^ { \circ } ,$ and $\Delta G ^ { \circ } ,$ which depends most strongly on temperature? When $\Delta G ^ { \circ }$ is calculated at temperatures other than $25 ^ { \circ } \mathrm { C } ,$ what assumptions are generally made concerning $\Delta H ^ { \circ }$ and $\Delta S ^ { \circ } ?$

Suppose that the coefficients of

$$F ( x ) = \sum _ { n = 0 } ^ { \infty } a _ { n } x ^ { n }$$

are periodic; that is, for some whole number M > 0, we have

$$a _ { M + n } = a _ { n }.$$

Prove that F(x) converges absolutely for |x| < 1 and that

$$F ( x ) = \frac { a _ { 0 } + a _ { 1 } x + \cdots + a _ { M - 1 } x ^ { M - 1 } } { 1 - x ^ { M } }$$

Graph the function. State the domain and range. g(x) = |2x - 3| + 1

For each equation, determine the substitution that should be made to write the equation in quadratic form. a.

$$x ^ { 4 } - 12 x ^ { 2 } + 27 = 0$$

Let y = ___. b.

$$x - 13 \sqrt { x } + 40 = 0$$

Let y = ___. c.

$$x ^ { 2 / 3 } + 2 x ^ { 1 / 3 } - 3 = 0$$

Let y = ___. d.

$$x ^ { - 2 } - x ^ { - 1 } - 30 = 0$$

Let y = ___. e.

$$( x + 1 ) ^ { 2 } - ( x + 1 ) - 6 = 0$$

Let y = ____.

Los dos universos, Clasifica las palabras segun las asocies con el universo de la literatura, de la vida rea o con ambos.

la ciencia, la magia, el recuerdo, la comunicacion, la imaginacion, la sociedad, el desarrollo, la lidentidad, la solidaridad, los descubrimientos, los logros, el sueno, la educacion, los pasatiempos, el tema, el espiritu, el personaje, la trama, la fantasia, el prejuicio, los valores, la fe, la realidad, la verdad.

Matrices P and Q are given.

$$P = \left[ \begin{array} { l l } { 3 } & { 2 } \\ { 6 } & { 9 } \\ { 1 } & { 0 } \end{array} \right] \quad Q = \left[ \begin{array} { r r } { - 3 } & { - 2 } \\ { - 6 } & { - 9 } \\ { 4 } & { 0 } \end{array} \right]$$

What is P - Q? A.

$$\left[ \begin{array} { r r } { - 6 } & { - 9 } \\ { - 8 } & { - 15 } \\ { 3 } & { 0 } \end{array} \right]$$

B.

$$\left[ \begin{array} { r r } { 0 } & { 5 } \\ { - 4 } & { - 3 } \\ { - 5 } & { 0 } \end{array} \right]$$

C.

$$\left[ \begin{array} { r r } { 0 } & { - 5 } \\ { 4 } & { 3 } \\ { 5 } & { 0 } \end{array} \right]$$

D.

$$\left[ \begin{array} { r r } { 6 } & { 4 } \\ { 12 } & { 18 } \\ { - 3 } & { 0 } \end{array} \right]$$