(a) At 4.2 K the heat capacity of Ag(s) is $0.0145\ \mathrm{JK}^{-1}\ \mathrm{mol} ^{-1}.$ Assuming that the Debye law applies, determine $S_{n}(4.2 K)-S_{n}(0)$ for silver. (b) At low temperatures the heat capacity of Ag(s) is found to obey the Debye law $C_{pm}=a T^{3},$ with $a=1.956 \times 10^{-4}\ \mathrm{JK}^{-1}\ \mathrm{mol}^{-1}.$ Determine $S_{n}(10 K)$ $-S_{\mathrm{n}}(0)$ for silver.

What happens to concavity when functions are added?
If $f(x)$ is concave up for all $x$ and $g(x)$ is concave down for all $x$, what can you say about the concavity of $f(x)+g(x)$ ? For example, what happens if $f(x)$ and $g(x)$ are both polynomials of degree $2$ ?

Graph the function $f(x)=\frac{x^{2}+1}{x}$ and answer the following questions. a. On what intervals is the function increasing? b. Where is the function concave up? c. Where is the function concave down? d. Is f even, odd, or neither? Justify your answer algebraically.

A laser used to repair a detached retina has wavelength of $532 \mathrm{~nm}$. The beam comes in short pulses, each lasting $25 \mathrm{~ms}$ and carrying $1.0 \mathrm{~J}$ of energy. (b) How many photons are in each pulse?

The school librarian got money to buy reference works on CDs. To find the cost $c$ of $n$ CDs, she used the function $c=32.99 n$. How much did she spend on 3 CDs?

For the function f(x)=$e^{-x^2/2}$,determine:- (a) the intervals on which f is increasing, (b) the intervals on which f is decreasing, $(c)$ the open intervals on which f is concave up, (d) the open intervals on which f is concave down, and (e) the x-coordinates of all inflection points.

Given $f(x) = (x - 2)^3$, (a) find the intervals where the function $f$ is increasing and where it is decreasing, (b) find the relative extrema of $f$, (c) find the intervals where the graph of $f$ is concave upward and where it is concave downward, and (d) find the inflection points, if any, of $f$.

Is the statement true or false? If the statement is true, explain how you know. If the statement is false, give a counterexample. Of two solids of revolution, the one with the greater volume is obtained by revolving the region in the plane with the greater area.

A gardener is transplanting flowers into a flowerbed. She has been working for an hour and has transplanted 14 flowers. She has 35 more flowers to transplant. If she works at the same rate, how many more hours will it take her?

Copy polygon U V W X Y Z and draw in all diagonals. Classify polygon U V W X Y Z as convex or concave.

Thomas Bouchard's study of twins is notable, because a. it demonstrated that peer influence is more important than parental influence in the development of personality traits. b. it proved that the influence of parental environment becomes more and more important as children grow into adults. c. he discovered almost unbelievable similarities between adult identical twins who had been separated near birth. d. fraternal twins showed almost as much similarity as identical twins when they reached adulthood. e. it provided evidence that heritability is less important than researchers previously suspected.

Examine the trigonometric function $f= 2x+\cot x ; (0, \pi)$. State where f is increasing, decreasing, concave up, and concave down, and state the x-coordinates of all inflection points. Check that your results are consistent with the graph of f generated with a graphing utility.

Roger has $40 to buy CDs. The CDs cost$5 each. He will definitely buy at least 3 CDs. How many CDs can Roger buy? Use inequalities to solve the problems.

a. Given any rectangle, describe ways to decompose the rectangle into two regions of equal area.
b. Given any right rectangular prism, describe how to decompose it into two solids with the same surface area.