Calculus Answers

find the area enclosed by the curve r^2=4cos theta

Given the area in the first quadrant bounded by x² = = 8y, the line

y-2 and the y-axis. What is the volume generated when this area is

revolved about the line y - 2 = 0?

Given the area in the first quadrant bounded by x² = 8y, the line

x=4 and the x-axis. What is the

the volume generated by revolving this

area about the y-axis?

Find the volume by revolving the hyperbola xy = 6 from x=2 to x=4

about the x-axis.

Find the length of arc of the curve 𝑦 = 𝑥 3⁄2 /√3 from (0, 0) to (4, √8 / 3 )

A ladder 20 meters long leans against a wall. If the bottom of the ladder is being pushed towards the wall at the rate of 20 m/min, how fast is the top of the ladder moving up the wall when the top of the ladder is 6 meters from the ground?

A rectangular gutter is formed by bending a 24 cm wide sheet of metal as shown. As a whole number, what is the height of a the gutter of maximum capacity?

Find equivalent functional definition for each of the following and draw a graph of the function.

f(x) = |x|•|x-1|

Find the equivalent functional definition for each of the following and draw a graph of the function.

f(x)= x+|x|.

Find equivalent functional definition for each of the following and draw a graph of a function.

f(x)=2x -|x| + |x-1|