Calculus Answers

Find the volume generated by revolving the area bounded by the lines x+2y=4, x=0 and y=0, about x-axis.

Fund the volume generated by revolving the area enclosed by the curves x^2+y^2=36 about the y-axis.

Find the area bound by the curves y=-x^2+4 and y=0.

Find the volume generated by revolving the area bounded by y=e^x, x=1, x=0, about y-axis. Sketch the curve indicating the generating area.

Find the area bounded by the curve y = x^3-12 x and the x-axis. Sketch the curve indicating the area bounded.

Analyze the function f(x) = - 2 cot 3x. Include:
- Domain and range
- Period
- Two Vertical Asymptotes

A cylindrical tank with a given volume V (V is constant) is to be made without a lid. The
material for the bottom costs five times as much per unit area as that for the sides. What
should be the ratio of the height to the radius for minimum cost?

find volume of solid generated by revolving the region bounded by y = √(x) and the lines y = 3 and x = 0 about the x-axis

statements is TRUE or FALSE

1 If y = eg(x) , then dy/dx = eg(x) / g(x) .

2. If for all x in (a, b), then f (x) is increasing on (a, b).

3. y = 6+2x-x2 has relative minimum at x=1, y=7.

4. ∫ xn dx= xn+1 / n+1 + C if n ≠ 1 .