Answer each question about the surface area S on a surface given by a positive function z = f(x, y) over a region R in the xy-plane. Explain each answer. (a) Is it possible for S to equal the area of R?

$(a)$ By what percentage does your rest mass increase when you climb $30 \mathrm{~m}$ to the top of a ten-story building? Are you aware of this increase? Explain. $(b)$ By how many grams does the mass of a $12.0 \mathrm{~g}$ spring with force constant $200 \mathrm{~N} / \mathrm{cm}$ change when you compress it by $6.0 \mathrm{~cm}$ ? Does the mass increase or decrease? Would you notice the change in mass if you were holding the spring? Explain.

Use the formula

$$\sin h+\sin 2 h+\sin 3 h+\cdots+\sin m h =\frac{\cos (h / 2)-\cos ((m+(1 / 2)) h)}{2 \sin (h / 2)}$$

to find the area under the curve y = sin x from x = 0 to $x=\pi / 2$ in two steps: Partition the interval $[0, \pi / 2]$ into n subintervals of equal length and calculate the corresponding upper sum U

Piecewise functions can sometimes be differentiable at a point where two pieces meet. For the function $f$, use one-sided limits to find the values of $a$ and $b$ that make $f$ differentiable at $x=2$.

$$f(x)=\left\{\begin{array}{l} a x^2+1, \quad \text { if } x<2 \\ -x^2+6 x+b, \quad \text { if } x \geq 2 \end{array}\right.$$

Plot the graph using Boolean variables to restrict the domain, and sketch the result.

Five selected transactions for the current month are indicated by letters in the following T accounts in a job order cost accounting system:

$$\begin{array}{l|r} &\text { Materials }\\ \hline&\text{A} \end{array}$$

$$\begin{array}{l|r} &\text { Wages Payable}\\ \hline&\text{B} \end{array}$$

$$\begin{array}{l|r} &\text { Factory Overhead}\\ \hline\text{A}&\text{C}\\ \text{B} \end{array}$$

$$\begin{array}{l|r} &\text { Work in Process}\\ \hline\text{A}&\text{D}\\ \text{B}\\ \text{C} \end{array}$$

$$\begin{array}{l|r} &\text { Finished Goodsd}\\ \hline\text{D}&\text{E}\\ \end{array}$$

$$\begin{array}{l|r} &\text { Cost of Goods Sold}\\ \hline\text{E} &\end{array}$$

Describe each of the five transactions.

Explain why the comparison test cannot be used to decide if the series converges or diverges. $\sum_{n=1}^{\infty} \sin n$

According to the Old Farmer's Almanac, in Detroit, Michigan, the number of hours of sunlight on the summer solstice is $13.65$ and the number of hours of sunlight on the winter solstice is 9.067. Look up the number of hours of sunlight for April 1 in the Old Farmer's Almanac and compare the actual hours of daylight to the results found in the previous part.

Use the tabulated values off to estimate the value of $\int_{0}^{6} f(x) d x$ \int_{0}^{6} f(x) d x regular partition with n=3 subintervals.

$$\begin{array}{|c|c|c|c|c|c|c|c|}\hline x & {0} & {1} & {2} & {3} & {4} & {5} & {6} \\ \hline f(x) & {20} & {22} & {26} & {30} & {34} & {38} & {40} \\ \hline\end{array}$$

For the underlined phrase or sentence, choose the revision that most improves the writing. Personally, I would rather read $\underline{\text{a poem without rhyme than with a tired old rhyme.}}$ A. a poem without rhyme than a tired old rhyming idea. B. a poem without rhyme than a tired old one C. a poem without rhyme than one with a tired old rhyme. D. Correct as is

Which of the three types of symmetries for polar graphs, and compare them to the symmetry of the graphs correspond to the symmetries with respect to Cartesian plane. the $x$-axis, $y$-axis, and origin?

Complete the following table to compare polynomial approximations of values of cosine x to the actual values of cosine x.

$$\begin{matrix} \text{x} & \ {1-\frac{x^{2}}{2 !}+\frac{x^{4}}{4 !}} & \ {\cos x}\\ \text{0.1} & \text{ } & \text{ }\\ \text{0.2} & \text{ } & \text{ }\\ \text{0.3} & \text{ } & \text{ }\\ \end{matrix}$$

A bag contains $2$ red, $6$ blue, $7$ yellow, and $3$ orange marbles. Once a marble is selected, it is not replaced. Find each probability.

$P(2$ yellows in a row then orange $)$

The __________ statement causes one or more statements to execute only when a Boolean expression is __________. a. else, false b. if, true c. if, false d. else, true

Have real roots that are rational. Use the Rational Zero Theorem to list all possible rational roots. Then graph the polynomial function in the given viewing rectangle to deter- mine which possible rational roots are actual roots of the equation.

$$6 x ^ { 3 } - 19 x ^ { 2 } + 16 x - 4 = 0 ; [ 0,2,1 ] \text { by } [ - 3,2,1 ]$$