Which of the following solids has a volume equal to the integral ∫0π∫0π/4∫01 ρ2 sinϕ dρdϕdθ{“version”:”1.1″,”math”:”∫0π∫0π/4∫01 ρ2 sinϕ dρdϕdθ”}

Which of the following solids has a volume equal to the integral ∫π2π∫01 r2 drdθ{“version”:”1.1″,”math”:”∫π2π∫01 r2 drdθ”}

Which of the following solids has a volume equal to the integral ∫π/23π/2∫01∫0r r dzdrdθ{“version”:”1.1″,”math”:”∫π/23π/2∫01∫0r r dzdrdθ”}

What is the approximate direction of the gradient vector at each of the following points?

Which of the following solids has a volume equal to the integral ∫0π∫01∫r1-r2 r dzdrdθ{“version”:”1.1″,”math”:”∫0π∫01∫r1-r2 r dzdrdθ”}

The function g(x, y) has tangent lines at the point (1, 2) with directions 2, 0, 8{“version”:”1.1″,”math”:”2, 0, 8″}  and 0, -13, 2{“version”:”1.1″,”math”:”0, -13, 2″}. Find  ∇g1,2{“version”:”1.1″,”math”:”∇g1,2″} . Write you answer using the greater and less than symbols for brackets, commas, numbers and no spaces. _______

Which point has the gradient vector with the smallest magnitude?

Briefly explain why antibiotics have no effect against viral infections (e.g. influenza).  To get full credit, you must show that: (1) you’re familiar with at least one of the ways in which antibiotics work, and (2) you can relate this to the processes involved in viral replication.

Which of the following solids has a volume equal to the integral ∫01∫-1-x21-x2∫x2+y21  1  dzdydx{“version”:”1.1″,”math”:”∫01∫-1-x21-x2∫x2+y21  1  dzdydx”}

Suppose that someone accidentally breathes in some tree pollen.  After a sufficient period of time passes, this person shows signs of being allergic to tree pollen.  In the space below, describe the entire sequence of events leading to the development of an allergic reaction to tree pollen. This sequence should start with being exposed to tree pollen and end with showing the symptoms/signs of tree pollen allergy.  Your answer should be comprehensive. Include as many details as you can about the cells, molecules, receptors and specific events that are involved in this process. Hint: It might be helpful for you to draw out this process first on your piece of scratch paper (similar to a concept map); you can then use that to help you answer this question. You won’t be asked to turn in the drawing on your scratch paper.