Calculus Answers

Find the cylindrical coordinates of the points where the cartesian coordinates are i)(3,3,4) ii) (√5,1,2)

The function f(x,y)={x^2y/x^4+y^2 (x,y) is not=0 0, (x,y)=0 is not continuous at (0,0)

f(x)=x² from x=0 to x=5

A cylindrical tank of radius 5 ft and height 9 ft is two-thirds filled with water. Find the work required to pump all the water over the upper rim.

(a). assuming that the tank is half-filled with water.

Assume that 10 ft-lb of work is required to stretch a spring 1 ft beyond its natural length. What is the spring constant?

A spring exerts a force of 100 N when it is stretched 0.2 m beyond its natural length. How much work is required to stretch the spring 0.8 m beyond its natural length?

Find the volume of the solid obtained by rotating the region enclosed by  𝑥=√6sin(𝑦)

 and 𝑥=0

 about the 𝑦-

axis over the interval 0≤𝑦≤𝜋.

The demand for a product, in dollars, is p = 2000-0.2x-0.01x² find the consumer surplus when the sales level is 250

Find the length of cardioid r = 1+sin"\\theta"

Find the area of the region that lies inside the circle r = 3sin"\\theta" and outside the cardioid r = 1+sin"\\theta"