Consider the following set of parametric equations: x ( t ) = 4 t y ( t ) = 8 t + 5 {“version”:”1.1″,”math”:”\begin{align*} x(t) &= 4\sqrt{t} \\ y(t) &= 8t+5 \end{align*}”} Part A — 5 points Find the derivative dydx{“version”:”1.1″,”math”:”dydx”} in terms of t{“version”:”1.1″,”math”:”t”} using parametric differentiation methods. Write your answer in the first answer box. Part B — 5 points Eliminate the parameter t{“version”:”1.1″,”math”:”t”} to obtain an equation for y{“version”:”1.1″,”math”:”y”} in terms of x{“version”:”1.1″,”math”:”x”}. Write your answer in the second answer box. Note: This part does not utilize the result from Part A. Part C — 5 points Using the original parametric equations as a reference, convert your answer from Part B from a function of t{“version”:”1.1″,”math”:”t”} to a function of x{“version”:”1.1″,”math”:”x”}. Take a standard derivative of this and write your answer in the third answer box.

Consider the function f(x) = x13{“version”:”1.1″,”math”:”f(x) = x13″} between y=0 and y=1{“version”:”1.1″,”math”:”y=0 and y=1″}. Find the surface area generated by revolving this arc about the y-axis. Note: Leave your answer in terms of π{“version”:”1.1″,”math”:”π”}.

Part A — 4 points Write a polar equation of the parabola whose focus is at the pole and vertex at 10,0{“version”:”1.1″,”math”:”10,0″}. Part B — 4 points Is the polar point 403,π3{“version”:”1.1″,”math”:”403,π3″} on the parabola?

Let the region R{“version”:”1.1″,”math”:”R”} be the area bounded by y = 2x-x2{“version”:”1.1″,”math”:”y = 2x-x2″}, the x-axis, and the y-axis. Find the volume of a solid whose base is R{“version”:”1.1″,”math”:”R”} and whose cross-sections parallel to the y-axis are squares. Note: Leave your answer as a fully-reduced fraction.

Evaluate the following integral: ∫ 1 e 3 1 x ln ⁡ x   d x {“version”:”1.1″,”math”:”\int\limits_1^{e^3} \frac{1}{x\sqrt{\ln x}} ~dx”}

Evaluate the following integral: ∫ 1 e 3 x 2 ln ⁡ x   d x {“version”:”1.1″,”math”:”\int\limits_1^e 3x^2 \ln x ~dx”}

Evaluate the following integral: ∫ 3 x + 11 x 2 − x − 6   d x {“version”:”1.1″,”math”:”\int \frac{3x+11}{x^2-x -6} ~dx”}Note: Write your answer as a single logarithm.

The region bounded by f(x) = 7sinx, x=0, x=π, and y=0{“version”:”1.1″,”math”:”f(x) = 7sinx, x=0, x=π, and y=0″} is rotated about the line x=π{“version”:”1.1″,”math”:”x=π”}. Set up, but do not evaluate, the volume of this solid of revolution.

Convert the polar coordinate 4,π6{“version”:”1.1″,”math”:”4,π6″} to Cartesian coordinates.

Ozone has the formula O3.  Which statement is correct concerning ozone?