Questions from General Calculus

Q: Economists use a cumulative distribution called a Lorenz curve to describe the

Economists use a cumulative distribution called a Lorenz curve to describe the distribution of income between households in a given country. Typically, a Lorenz curve is defined on [0, 1] with endpoin...

Q: Use the method of cylindrical shells to find the volume generated by

Use the method of cylindrical shells to find the volume generated by rotating the region bounded by the given curves about the y-axis. Sketch the region and a typical shell.

Q: Use the method of cylindrical shells to find the volume generated by

Use the method of cylindrical shells to find the volume generated by rotating the region bounded by the given curves about the y-axis. Sketch the region and a typical shell.

Q: Let V be the volume of the solid obtained by rotating about

Let V be the volume of the solid obtained by rotating about the y-axis the region bounded by y = √x and y = x2. Find V both by slicing and by cylindrical shells. In both cases draw a diagram to explai...

Q: A cone of radius r centimeters and height h centimeters is lowered

A cone of radius r centimeters and height h centimeters is lowered point first at a rate of 1 cm/s into a tall cylinder of radius R centimeters that is partially filled with water. How fast is the wat...

Q: Use the method of cylindrical shells to find the volume of the

Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by the given curves about the x-axis.

Q: Use the arc length formula (2) to find the length

Use the arc length formula (2) to find the length of the curve y – 2x - 5, -1 < x < 3. Check your answer by noting that the curve is a line segment and calculating its length by the distance formula....

Q: Find the exact length of the curve. y = √

Find the exact length of the curve. y = √x – x2 + sin-1 (√x)

Q: Find the exact length of the curve. y = 1

Find the exact length of the curve. y = 1/4x2 – 1/2 lnx, 1 < x < 2

Q: Find the exact length of the curve. x = a

Find the exact length of the curve. x = a (cos θ + θ sin θ), y = a (sin θ – θ cos θ), 0 < θ < π