Which of the following solids has a volume equal to the integral ∫-11∫01-y2∫1-y2-x21  dzdxdy{“version”:”1.1″,”math”:”∫-11∫01-y2∫1-y2-x21  dzdxdy”}

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”}