Evaluate each of the following in $x + iy$ form, and compare with a computer solution. $\ln (-i)$

Find the intervals on which the graph of f is concave upward, the intervals on which the graph of f is concave downward, and the x coordinates of the inflection points. $f(x)=x^{4}+6 x$

Use the preliminary test to decide whether the following series are divergent or require further testing. Careful: Do not say that a series is convergent; the preliminary test cannot decide this. $\sum_{n=1}^{\infty} \frac{\ln n}{n}$

Let y=f(x) be a polynomial function with local minima at x=a and x=b, a<b. Must f have at least one local maximum between a and b? Justify your answer.

The triple bottom line includes what three main dimensions?

Helium gas is sold in steel tanks that will rupture if subjected to tensile stress greater than its yield strength of $5 \times 10^{8} \mathrm{N} / \mathrm{m}^{2}$ If the helium is used to inflate a balloon, could the balloon lift the spherical tank the helium came in? Justify your answer. Suggestion: You may consider a spherical steel shell of radius r and thickness t having the density of iron and on the verge of breaking apart into two hemispheres because it contains helium at high pressure.

You are working in your first job at a clothing retailer. You arrive at work one evening wearing a political t-shirt after attending a political club at school that you are part of. You change into your uniform and work your shift. The following day, the schedule comes out and you see that your hours were drastically reduced. You ask your manager about it, and they tell you that the store doesn’t support or agree with your political affiliations.

Write the terms for each series and evaluate the sum, given that $x_{1}=-2, x_{2}=-1, x_{3}=0$, $x_4=1$, and $x_5=2$. $\sum_{i=1}^{5} x_{i}$

Review the notes you took on Life of Peter the Great and the image of Peter the Great Cutting a Boyar’s Beard and respond to the following questions: For the image, explain how the historical context affected the creation of the etching Peter the Great Cutting a Boyar’s Beard. Using the Life of Peter the Great, identify the author’s point of view as expressed in this early history of Peter the Great. Explain how the author’s point of view affects the image as a reliable source of evidence. How did both Akbar the Great and Peter the Great centralize their power? Explain.

Evaluate dy and $\Delta y$ for each function for the indicated values. $y=f(x)=75\left(1-\frac{2}{x}\right) ; x=5, d x=\Delta x=-0.5$

A spherical balloon of volume $4.00 \times 10^{3} \mathrm{cm}^{3}$ contains helium at a pressure of $1.20 \times 10^{5} \mathrm{Pa}$. How many moles of helium are in the balloon if the average kinetic energy of the helium atoms is $3.60 \times 10^{-22} \mathrm{J}$?

Verify (6.14) by multiplying the matrices and using trigonometric addition formulas.

A proton moving at $4.00 \times 10^{6} \mathrm{m} / \mathrm{s}$ through a magnetic field of magnitude 1.70 T experiences a magnetic force of magnitude $8.20 \times 10^{-13} \mathrm{N}$. What is the angle between the proton's velocity and the field?

What three factors would influence your evaluation as to whether a company’s current ratio is good or bad?