Sketch the Lorenz curve y = L(x) and find the corresponding Gini index. $L(x)=x^{1.2}$

Compute each limit or state that it does not exist. Use the tools developed in this section to justify each conclusion.

$$\begin{array} { l } { \text { (a) } \lim _ { x \rightarrow 2 } \frac { | x - 2 | } { x - 2 } } \\ { \text { (b) } \lim _ { x \rightarrow 7 / 4 } \frac { | x - 2 | } { x - 2 } } \\ { \text { (c) } \lim _ { x \rightarrow 0 } ( - 1 ) ^ { [ [ 1 / x ] ] } } \\ { \text { (d) } \lim _ { x \rightarrow 0 } \sqrt [ 3 ] { x } ( - 1 ) ^ { [ [ 1 / x ] ] } } \end{array}$$

Report on the interest rates paid on investments by a savings and loan company and the compounding period for (a) Passbook savings. (b) 6-month money market. (c) 12-month money market. (d) 5-year money market.

Factor each polynomial completely. If a polynomial cannot be factored, state that it is irreducible. $5 x ^ { 2 } - 10 x - 40$

describe how to transform the graph of ƒ into the graph of g. Sketch the graphs by hand and support your answer with a grapher.

$$ƒ(x) = 0.6^x, g(x) = 2*0.6^3x$$

Ordinary household electric lines in North America usually operate at 120 V. Why is this a desirable voltage, rather than a value considerably larger or smaller? On the other hand, automobiles usually have 12-V electrical systems. Why is this a desirable voltage?

In the accompanying figure, two ropes are attached to a large In the accompanying figure, two ropes are attached to a large $\langle- 164,115\rangle$ pounds on the crate and rope B exerts a force of $\langle 177,177\rangle$ pounds on the crate. If the crate weighs 275 pounds, what is the net force acting on the crate? Based on your answer, which way will the crate move?

Fractional powers can give surprising resurts when used with negative bases. Answer the following questions using whal you now know about how to rewrite fractional powers: and your mental math skills - avoid using your calculator. Show or explain why

(- 100)? 7 has no reat solution but (- 100)? 4 = 10 even though 2 can be reduced to $\frac { 1 } { 2 }$

The two branches of the parent reciprocal function $f(x)=\frac{1}{x}$ are symmetric about what line?

The following integrals require a preliminary step such as long division or a change of variables before using the method of partial fractions. Evaluate these integrals.

$$\int \frac { d x } { 1 + e ^ { x } }$$

find the sum of the finite arithmetic sequence. -5 + (-3) + (-1) + 1 + 3 + 5

Find the number of sides of each regular polygon. The sum of the measures of interior angles is $2160^{\circ}$.

Find the inverse of each matrix, if it exists.

$$\left[\begin{array}{ll}{2} & {1} \\ {4} & {3}\end{array}\right]$$

Let V be a vector space. Prove $c \bigodot 0 = 0$ for any scalar c and $(-1) \bigodot u = -u$.