f(x) is continuous on $(-\infty, \infty)$. Use the given information to sketch the graph of f.

$$\begin{aligned}&f(0)=2, f(1)=0, f(2)=-2\\&f^{\prime}(0)=0, f^{\prime}(2)=0\\&f^{\prime}(x)>0 \mathrm\ { on }\ (-\infty, 0) \mathrm\ { and }\ (2, \infty)\\&f^{\prime}(x)<0 \mathrm\ { on }\ (0,2)\\&f^{\prime \prime}(1)=0\\&f^{\prime \prime}(x)>0 \mathrm\ { on }\ (1, \infty)\\&f^{\prime \prime}(x)<0 \mathrm\ { on }\ (-\infty, 1)\end{aligned}$$

Test the following series for convergence or divergence. Decide for yourself which test is easiest to use, but don’t forget the preliminary test. Use the facts stated above when they apply. $\sum_{n=1}^{\infty} \frac{(-1)^{n}}{2^{\ln n}}$

Solve each set of equations by the method of finding the inverse of the coefficient matrix.

$$\left\{\begin{array}{rr} x-y+z= 4 \\ 2 x+y-z= -1 \\ 3 x+2 y+2 z= 5 \end{array}\right.$$

For the situation described in the previous question, which cart experiences the greater change in kinetic energy? Each cart has the same change in kinetic energy.

Solve each equation using completing the square. $x^{2}-7 x+12=0$

A harmonic oscillator is described by the function x(t) = (0.200 m) cos (0.350t). Find the oscillator's position.

A person's basal metabolic rate (BMR) is the rate at which energy is expended while resting in a neutrally temperate environment. A typical BMR is $7.00 \times 10^{6}$ J/day. Convert this BMR to units of watts. Find the rate of change of the object's height in m/s.

A cosmic ray travels 60 km through the earth’s atmosphere in $400 \mu \mathrm{s}$, as measured by experimenters on the ground. How long does the journey take according to the cosmic ray?

A person standing 1.00 m from a portable speaker hears its sound at an intensity of $7.50 \times 10^{-3} \mathrm{W} / \mathrm{m}^{2}$. Find the decibel level at a distance of 35.0 m.

The rainbow of visible colors in the electromagnetic spectrum varies continuously from the longest wavelengths (the reddest colors) to the shortest wavelengths (the deepest violet colors) our eyes can detect. Wavelengths near 655 nm are perceived as red. Those near 515 nm are green and those near 475 nm are blue. Calculate the frequency of light with a wavelength of 475 nm.

Use Tukey's method to make all the pairwise comparisons for the heart rate data at the 0.05 level of significance.

An air-filled parallel-plate capacitor with capacitance $C_0$ stores charge Q on plates separated by distance d. The potential difference across the plates is $\Delta V_{0}$ and the energy stored is $P E_{C, 0}.$ If the capacitor is disconnected from its voltage source and the space between the plates is then filled with a dielectric of constant K = 2.00, evaluate the ratios $C_{\text {new }} / C_{0}$.

In the blank space beside each numbered balance sheet item, enter the letter of its balance sheet classification. If the item should not appear on the balance sheet, enter a Z in the blank.

$$\begin{matrix} \text{A. Current assets} & \text{E. Current liabilities}\\ \text{B. Long-term investments} & \text{F. Long-term liabilities}\\ \text{C. Plant assets} & \text{G. Equity}\\ \text{D. Intangible assets}\\ \end{matrix}$$

$$\begin{matrix} \text{\_\_\_\_\_\_\_\_\_1. Commissions earned} & \text{\_\_\_\_\_\_\_\_\_ 11. Rent receivable}\\ \text{\_\_\_\_\_\_\_\_\_ 2. Interest receivable} & \text{\_\_\_\_\_\_\_\_\_ 12. Salaries payable}\\ \text{\_\_\_\_\_\_\_\_\_ 3. Long-term investment in stock} & \text{\_\_\_\_\_\_\_\_\_ 13. Income taxes payable}\\ \text{\_\_\_\_\_\_\_\_\_ 4. Prepaid insurance} & \text{\_\_\_\_\_\_\_\_\_ 14. Common stock}\\ \text{\_\_\_\_\_\_\_\_\_ 5. Machinery} & \text{\_\_\_\_\_\_\_\_\_ 15. Office supplies}\\ \text{\_\_\_\_\_\_\_\_\_ 6. Notes payable (due in 15 years)} & \text{\_\_\_\_\_\_\_\_\_ 16. Interest payable}\\ \text{\_\_\_\_\_\_\_\_\_ 7. Copyrights} & \text{\_\_\_\_\_\_\_\_\_ 17. Rent revenue}\\ \text{\_\_\_\_\_\_\_\_\_ 8. Current portion of long-term note payable} & \text{\_\_\_\_\_\_\_\_\_ 18. Notes receivable (due in 120 days)}\\ \text{\_\_\_\_\_\_\_\_\_ 9. Accumulated depreciation—Trucks} & \text{\_\_\_\_\_\_\_\_\_ 19. Land (used in operations)}\\ \text{\_\_\_\_\_\_\_\_\_ 10. Office equipment} & \text{\_\_\_\_\_\_\_\_\_ 20. Depreciation expense—Trucks}\\ \end{matrix}$$

Equipment that was purchased by Newport Corporation for making pneumatic vibration isolators cost $90,000 two years ago. It has a market value that can be described by the relation$90,000 − 8000k, where k is the years from time of purchase. The operating cost for the first 5 years is $65,000 per year, after which it increases by$6300 per year. The asset’s salvage value was originally estimated to be $7000 after a predicted 10-year useful life. Determine the values of P, S, and AOC if (a) a replacement study is done now and it is assumed that the equipment will be kept a maximum of only 1 more year, and (b) a replacement study is done 1 year from now and it is assumed that the equipment will be kept a maximum of only 1 more year after that.