Calculus I, Fall 2014

Quiz 5

Dec 23, 2014 Show all details.

1. A torus (donut) is generated by revolving the disk (x − 2)^{2} + y^{2} ≤ 1 around the y axis. Find the volume of the torus.

2. Find the surface area of the torus in problem 1.

3. Find the length of the curve y = ∫_{0}^{x} \sqrt{cos t} dt from x = 0 to x = \frac{π}{2}.

4. Find the solutions for \frac{dy}{dx} = 3x^{2}e^{−y}.

5. Find the solution for x\frac{dy}{dx} + y = e^{x} on x > 0 with y(1) = 1.

Calculus I, Fall 2014

Quiz 5

Dec 23, 2014 Show all details.

1. A torus (donut) is generated by revolving the disk (x − 2)^{2} + y^{2} ≤ 1 around the y axis. Find the volume of the torus.

2. Find the surface area of the torus in problem 1.

3. Find the length of the curve y = ∫_{0}^{x} \sqrt{cos t} dt from x = 0 to x = \frac{π}{2}.

4. Find the solutions for \frac{dy}{dx} = 3x^{2}e^{−y}.

5. Find the solution for x\frac{dy}{dx} + y = e^{x} on x > 0 with y(1) = 1.