Essay – Craft an essay with a defensible thesis that directly addresses only one of the prompts.   A.  What are the most important and applicable lessons learned from the turbulent events during the years 1914–1945?   OR   B.  To what extent was Nazism inevitable?   OR   C. In lecture we discussed how WWI and WWII were two parts of one larger conflict. Build as essay that explores this relationship.       Essay Outline   I. THESIS (Should make a defensible claim that directly addresses the question and highlights specific themes/arguments.)     II. Themes/Arguments (Evidence should validate your themes/arguments in answering your thesis)                     – Theme/Argument  A                                     – Supporting evidence                                      – Supporting evidence                                     – Supporting evidence                                     – etc.                     – Theme/Argument  B                                     – Supporting evidence                                      – Supporting evidence                                     – Supporting evidence                                     – etc.                     – Theme/Argument  C                                     – Supporting evidence                                      – Supporting evidence                                     – Supporting evidence                                     – etc.                     – Etc.

Treating an auto-immune disease such as Ulcerative Colitis or Lupus by infecting the diseased person with a tapeworm or a pinworm would be in agreement with which of the following ideas?

Which has an older TMRCA? 

Come up with your own non-constant conservative vector field F→\style{font-size:35px}{\vec{F}}. Show that is it conservative. Then, find the work done by F→\style{font-size:35px}{\vec{F}} over the curve starting at (5,5)\style{font-size:35px}{(5,5)}, looping around the arrow on the x-\style{font-size:35px}{x-}axis, visiting Neptune, traveling to another universe, then coming back and ending up back at (5,5)\style{font-size:35px}{(5,5)}.Hint: work can be represented by ∫CF→∙ dr→\style{font-size:35px}{\int_C{\vec{F}\bullet\ d\vec{r}}}.

Evaluate the integral ∫∫Q∫xz dV\style{font-size:35px}{\int\int\limits_Q\int{xz\ dV}} where Q\style{font-size:35px}{Q} is the quarter of the unit sphere x2+y2+z2=1\style{font-size:35px}{x^2+y^2+z^2=1} in octants I and IV (i.e. with 0≤x≤1\style{font-size:35px}{0\leq x\leq 1}, -1≤y≤1\style{font-size:35px}{-1\leq y\leq 1}, and 0≤z≤1\style{font-size:35px}{0\leq z\leq 1}).

Evaluate ∫C(-y-2x) dx+(2x+8y) dy\style{font-size:35px}{\int_C{(-y-2x)\ dx + (2x+8y)\ dy}} where C\style{font-size:35px}{C} is the curve y=x2\style{font-size:35px}{y=x^2} from (0,0)\style{font-size:35px}{(0,0)} to (2,4)\style{font-size:35px}{(2,4)}, by first parametrizing C\style{font-size:35px}{C} as r→(t)\style{font-size:35px}{\vec{r}(t)}.

Let SS be given by z=9-x2-y2z=9-x^2-y^2 with z≥0z\geq 0 with CC as its counterclockwise boundary curve. Let F→(x,y,z)=\vec{F}(x,y,z)=.Use Stoke’s Theorem to find the line integral ∫CF→∙dr→\int_C{\vec{F}\bullet d\vec{r}} by first converting it to the flux integral as ∫S∫(∇×F→)∙N→ dS\int_S\int{(\nabla\times\vec{F})\bullet \vec{N}\ dS}.

Set up an integral in cylindrical coordinates that represents the volume to the right of the cone y=x2+z2y=\sqrt{x^2+z^2} and left of the plane y=4y=4. Include bounds for your integral, but no need to evaluate.

Set up an integral in spherical coordinates that represents the volume of the sphere x2+y2+z2=25x^2+y^2+z^2=25 in octant VI. Include bounds for your integral, but no need to evaluate.

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