An alternate definition of absolute value is

$$|a|=\left\{\begin{array}{l} a \text { if } a \text { positve or zero. } \\ -a \text { if } a \text { is negative. } \end{array}\right.$$

(NOTE: $-a$ is the opposite of $a$.) Using this definition, calculate the following values.

$$|-x| \text { if } -x>0$$

The "natural" way to graph y=sin x or y=cos x is to measure x in radians and use the same real-number scale on both axes. Use this method to sketch the graph of y=sin x. (Note that $\pi$ is a little more than 3 units on the x-axis.)

You can combine the use of context clues with your knowledge of this prefix to make intelligent guesses about the meanings of words. All of the sentences below contain a word formed with the prefix dis-. Read the sentences and write down what you think the word in italics means. Then check your definition with the one you find in the dictionary, remembering to choose the definition that best fits the sentence. The Dickens character Uriah Heep $dissimulated$, hiding his evil intentions. My definition.$\rule{30cm}{0.15mm}$ Dictionary definition$\rule{30cm}{0.15mm}$

U.S. postal rules require that the length plus the girth of a package cannot exceed 84 inches. Find the dimensions of the rectangular package of greatest volume that can be mailed. [Note that 84 = (length) + (girth) = l + (2x + 2y).

Using Different Sentence Openers. Each of the following sentences can be rewritten with n different opener. Look for a modifier, phrase, or clause that can be placed at the beginning of the sentence. The audience stood from the band's first note to its last.

Evaluate the following expression using the definition of common logarithms.

$$\log 10$$

You can combine the use of context clues with your knowledge of this prefix to make intelligent guesses about the meanings of words. All of the sentences below contain a word formed with the prefix dis-. Read the sentences and write down what you think the word in italics means. Then check your definition with the one you find in the dictionary, remembering to choose the definition that best fits the sentence. Many respectable business people refused to deal with the $disreputable$ merchant. My definition$\rule{30cm}{0.15mm}$ Dictionary definition$\rule{30cm}{0.15mm}$

Make the given changes in the integrands of the indicated examples of this section. Then write out the equation that shows the partial fractions (like those opposite NOTE) that would be used for the integration.

In previous example, change the numerator from $1$ to $2$.

A friend says that the recursive definition for the geometric sequence 1, -1, 1, -1, 1, ... is $A(n)=1\cdot (-1)^{n-1}$. Do you agree? If so, write the explicit formula for the sequence. If not, write the correct recursive definition.

Read each sentence to determine the meaning of the italicized word. Write the meaning you obtain from the context clues. Then look up the word in the dictionary and write the most suitable formal definition. Most people had to pay for the tote bag, however those who made a donation to the charity received it $gratis$. My definition $\rule{10cm}{0.15mm}$ Dictionary definition $\rule{10cm}{0.15mm}$

With the help of Formula $(15)$ of Section $4.9$ find the standard matrix for a rotation of $180^{\circ}$ about the axis determined by the vector $v=(2,2,1)$. $[$Note: Formula $(15)$ requires that the vector defining the axis of rotation have length $1.]$

The terms "vertical" and "horizontal" are frequently used in physics. Give operational definitions for these two terms. An operational definition defines a term by how it is measured or determined. Your definition should apply equally well in a laboratory or on a steep mountainside.

Identify the idiom in each sentence. Then, write a definition for each one. If you are unsure of the meaning of the word or phrase, check your definition in a print or online dictionary. Jurors must try to keep an open mind during the trial.

The sentence below in this exercise contains a word beginning with one of the three prefixes in this lesson. When appropriate, the root word and its meaning are given in parentheses after the sentence. Step 1: Taking the context into consideration, write your own definition of the word. Step 2: Write the dictionary definition of the word. Step 3: Write a sentence of your own in which you use the word correctly.

The workers were confused when the manager countermanded her previous order. (Latin root word: mandare, "to command")

YOUR DEFINITION ______________________________________________________________________________________________________________________

DICTIONARY DEFINITION ______________________________________________________________________________________________________________________

SENTENCE ______________________________________________________________________________________________________________________