A(n) ______ is a special value that marks the end of a series of values.

In the following sentence, underline the two prepositional phrases. Draw an arrow from each phrase to the word or words it modifies. Then, on the line provided, Identify each phrase by writing $A D J$ for adjective or $A D V$ for adverb.

___________ I have developed some of those ideas into short stories.

The area under the curve $y=\sqrt{x}$ bounded below by the x-axis and on the right by x = 4 is $\frac{16}{3}$ square units. Using the ideas presented in this section, what do you think is the area under the curve of $y=\sqrt{-x}$ bounded below by the x-axis and on the left by x = - 4? Justify your answer.

Explain the mistake made :$\newline \textbf{Exercise:}$ $\newline$ The terminal side of an angle $\theta$ in standard position passes through the point (1, 2). Calculate $\sin {\theta}$.

$$\textbf {Solution:}$$

1. Label the coordinates.

$$x = 1, y = 2$$

2. Calculate $r$.

$$r = 1^2 + 2^2 = 5$$

3. Use the definition of sine.

$$\sin{\theta}=\frac{y}{r}$$

4. Substitute y = 2, r = 5.

$$\sin{\theta}=\frac{2}{5}$$

The is incorrect. Identify the Mistake made above.

Distinguish between porosity and permeability. Contrast aquifer and aquitard .

Compare and contrast the germination of bean seeds and corn seeds.

Compare and contrast the following pair of terms. Mercury, Jupiter

Identifying Adverb Clauses. Each of the following sentences contains an adverb clause. Underline each adverb clause and circle the verb, adjective, or adverb each clause modifies. While I generally respect your ideas. I cannot agree with your present plan.

Carefully re-read lines $14-2$ of the poem, referring to the painting on page 1046 as you do so. Do you think Auden has correctly interpreted Bruegel's painting? Use evidence from both the text and the painting to support your ideas.

Find the Maclaurin series for the function. $h(x)=x \cos x$

Suppose that

$$\mathbf { F }$$

is defined on

$$\mathbf { R } ^ { 3 }$$

and that

$$\oint _ { \mathcal { C } } \mathbf { F } \cdot d \mathbf { r } = 0$$

for all closed paths

$$\mathcal { C }$$

in

$$\mathbf { R } ^ { 3 }.$$

Prove:

$$\mathbf { F }$$

is path-independent; that is, for any two paths

$$\mathcal { C } _ { 1 }$$

and

$$\mathcal { C } _ { 2 }$$

in

$$\mathcal { D }$$

with the same initial and terminal points,

$$\int _ { \mathcal { C } _ { 1 } } \mathbf { F } \cdot d \mathbf { r } = \int _ { \mathcal { C } _ { 2 } } \mathbf { F } \cdot d \mathbf { r }$$

Find the Maclaurin series for the function. 7 cos (-x)

In the movie Superman, Lois Lane falls from a building and is caught by the diving superhero. Assuming that Lois, with a mass of $50.0 \mathrm{~kg}$, is falling at a terminal velocity of $60.0 \mathrm{~m} / \mathrm{s}$, how much force does Superman exert on her if it takes $0.100 \mathrm{~s}$ to slow her to a stop? If Lois can withstand a maximum acceleration of $7 g$ s, what minimum time should it take Superman to stop her after he begins to slow her down?

Find the Maclaurin series of the function. $f ( x ) = \frac { \sin x } { x }$