Find and interpret the value of the expression in practical terms. Let C(t) be the concentration of carbon dioxide in parts per million (ppm) in the air as a function of time, t, in months since December 1, 2005: $C ( t ) = 3.5 \sin \left( \frac { \pi t } { 6 } \right) + 381 + \frac { t } { 6 }.$ C'(36)

Construct a difference table to predict the next term of each sequence. 17, 15, 25, 53, 105, 187, ...

How can you derive the Law of Sines for angles B and C?

Write the indicated theorems as a biconditional statement. Theorem 8.4, page 515 and Theorem 8.8, page 522

What elements in "The Masque of the Red Death" illustrate what is meant by King's metaphor of a closed, forbidden door on page 446?

Find the directional derivative of

$$f(x, y) = x^2 + 2y^2$$

at x = 2 and y = 2 in the direction of h = 2i + 3j

The function

$$f(x)=ln(e^x)$$

is one of our twelve basic functions written in another form. Graph the function and identify which basic function it is.

The sum of the first n terms of an arithmetic sequence is

$$S _ { n } = 3 n ^ { 2 } - 2 n$$

. Find the nth term,

$$\mathcal { U } _ { n }$$

.

Solve the equation.

$$x^2+x+11=5x-8$$

Write each number in scientific notation. -0.00000000405

Solve the equation. Give the exact solution and an approximate solution to four decimal places, when appropriate.

$$e ^ { 0.08 t } = 4$$

A sequence is an infinite, ordered list of numbers that is often defined by a function. For example, the sequence {2, 4, 6, 8, ...} is specified by the function f(n)=2n, where n=1, 2, 3,... The limit of such a sequence is $\lim _ { n \rightarrow \infty } f ( n )$, provided the limit exists. All the limit laws for limits at infinity may be applied to limits of sequences. Find the limit of the following sequences or state that the limit does not exist. $\left\{ 0 , \frac { 1 } { 2 } , \frac { 2 } { 3 } , \frac { 3 } { 4 } , \dots \right\}$, which is defined by f(n)=$\frac { n - 1 } { n }$, for n=1, 2, 3, ...

Complete each statement by writing the correct word or words. At equilibrium, both the forward and the reverse reactions continue, but the ______ of the reactants stay the same.

Find the LCD. List the multiples or use prime factorization. $\frac { 7 } { 21 } , \frac { 3 } { 9 },$ and $\frac { 5 } { 7 }$