Find the most general antiderivative of the function. (Check your answer by differentiation.)

$$f ( x ) = e ^ { 2 }$$

Three vertices of a rectangle are located at (3, 1), (-2, 1), and (-2, -3). What is the area of the rectangle?

Find each product.

$$( 9 - 5 x ) ^ { 2 }$$

Although Social Security is a problem, some projections indicate that there's a much bigger time bomb ticking in the federal budget, and that's Medicare. In 2000, the cost of Social Security was 5.48% of the gross domestic product, increasing by 0.04% of the GDP per year. In 2000, the cost of Medicare was 1.84% of the gross domestic product, increasing by 0.17% of the GDP per year. Write a function that models the cost of Medicare as a percentage of the GDP x years after 2000.

Factor the polynomial.

$$2 s ^ { 3 } - 3 s ^ { 2 } + 18 s - 27$$

Show that if

$$(x_n)$$

is an unbounded sequence, then there exists a properly divergent subsequence.

Consider the function f(x) = x - cos x. Starting with x0 = 1, generate a sequence x1, x2, x3, . . . where xn = cos(xn-1). For example, x0 = 1, x1 = cos(x0), x2 = cos(x1), x3 = cos(x2), ... What value does the sequence approach?

Find

$$S _ { n }$$

for each geometric series.

$$243 + 81 + 27 + \ldots \text { to } 5 \text { terms }$$

Find the length of the curve over the given interval. Polar Equation: r = 8 Interval: 0 ≤ θ ≤ 2π

Briefly explain the significance of Jim Crow.

Express the given function h as a composition of two functions f and g so that

$$h ( x ) = ( f \circ g ) ( x )$$

$$h ( x ) = | 2 x - 5 |$$

A classmate states, “All compounds containing H atoms are acids, and all compounds containing OH groups are bases.” Do you agree? Give examples.

Complete each equation.

$$\left( m ^ {\square} \right) ^ { 3 } = m ^ { - 12 }$$

Use these matrices to answer.

$$A = \left[ \begin{array} { r r r } { 3 } & { - 6 } & { 1 } \\ { - 8 } & { 2 } & { 0 } \end{array} \right] \quad B = \left[ \begin{array} { r r } { 5 } & { - 7 } \\ { - 3 } & { 2 } \end{array} \right] \quad C = \left[ \begin{array} { c c } { 4 } & { 10 } \\ { - 1 } & { - 3 } \end{array} \right]$$

Find C – B.