The reciprocal of a whole number is a fraction with __________ in the numerator.

Find the $x$-coordinate(s) of the point(s) on the graph of the function at which the tangent line has the indicated slope.

$$f(x)=\cot x ; \quad m_{\tan }=-2$$

Choose the correct answer.

Please let employees know if you would like them to dress (a) nicer, (b) more nicely for business meetings.

Name the following compounds: (a) $\mathrm{SnO}_2$ (b) $\mathrm{Ca}(\mathrm{CN})_2$ (c) $\mathrm{Na}_2 \mathrm{CO}_3$ (d) $\mathrm{Cu}_2 \mathrm{SO}_4$ (e) $\mathrm{Ba}(\mathrm{OH})_2$ (f) $\mathrm{Fe}\left(\mathrm{NO}_3\right)_2$

Graph each function. Based on the graph, state the domain and the range and find any intercepts.

$$f(x)=\left\{\begin{array}{ll}{-\ln x} & {\text { if } 0<x<1} \\ {\ln x} & {\text { if } x \geq 1}\end{array}\right.$$

Calculate.

$$\int_0^{\pi / 2} \int_0^{3 \sin \theta} r^2 d r d \theta$$

Express the sums in sigma notation. The form of your answer will depend on your choice for the starting index. $1+2+3+4+5+6$

Graph each function. Based on the graph, state the domain and the range and find any intercepts.

$$f(x)=\left\{\begin{array}{ll}{\ln x} & {\text { if } 0<x<1} \\ {-\ln x} & {\text { if } x \geq 1}\end{array}\right.$$

Calculate Many highways have a speed limit of $55 \mathrm{mi} / \mathrm{h}$. (a) Is this speed greater than, less than, or equal to $55 \mathrm{~km} / \mathrm{h}$ ? Explain. (b) Find the speed limit in $\mathrm{km} / \mathrm{h}$ that corresponds to $55 \mathrm{mi} / \mathrm{h}$.

Check Your Understanding Which of the following compounds would be soluble in water at room temperature?

(a) $\mathrm{NH}_4 \mathrm{Cl}$,

(b) $\mathrm{KOH}$,

(c) $\mathrm{Ca}\left(\mathrm{CH}_3 \mathrm{COO}\right)_2$,

(d) $\mathrm{Ba}_3\left(\mathrm{PO}_4\right)_2$

(Continuation of the previous Exercise) Suppose $\mathbf{r}(t)=f(t) \mathbf{i}+$ $g(t) \mathbf{j}+h(t) \mathbf{k}$ and $f, g$, and $h$ have derivatives through order three. Use the results of the Exercise discussed before to show that

$$\frac{d}{d t}\left(\mathrm{r} \cdot \frac{d \mathbf{r}}{d t} \times \frac{d^2 \mathbf{r}}{d t^2}\right)=\mathrm{r} \cdot\left(\frac{d \mathbf{r}}{d t} \times \frac{d^3 \mathbf{r}}{d t^3}\right) .$$

(Hint: Differentiate on the left and look for vectors whose products are zero.)

Directors are expected to use their best judgment in managing the corporation. What must directors do to avoid liability for honest mistakes of judgment and poor business decisions?

Examine the shape of the horizon at the Apollo 17 landing site. What processes shape mountains on Earth that have not affected mountains on the Moon?

Graph each function. Based on the graph, state the domain and the range and find any intercepts.

$$f(x)=\left\{\begin{array}{ll}{\ln (-x)} & {\text { if } x \leq-1} \\ {-\ln (-x)} & {\text { if }-1<x<0}\end{array}\right.$$