Robert E.

For f(x, y) = x2 - 12xy + y2 + 1, finda) The direction of the maximum rate of change at P(1,1)b) The direction of the minimum rate of change at P(1, 1)

If a snowball melts so that its surface area decreases at a rate of 7 cm2/min, find the rate at which the diameter decreases when the diameter is 12 cm.

Find all solutions to 2sin(θ)=√2 on the interval 0≤θ<2π θ =    Give your answers as exact values, as a list separated by commas.

Curve equation 2x^2+3y^2−4xy=36.

For the function f(x,y) = e^( -(5x^2 + 6y^2) ), what are the shape of the level curves?A collection of equally spaced parallel lines,A collection of unequally spaced parallel lines,A collection of... more

Paul is looking at his track team’s times for the 5K races they’ve run this year. He finds that the values are normally distributed, with a mean of 22.5 minutes and a standard deviation of 2... more

Use cylindrical shells to find the volume of the solid formed by rotating the area between the graph of x=y^(1/8) and x=0, 0≤y≤1. y18andx=0,0≤y≤1 about the x-axis. Volume = ∫ upper is 1, lower is 0... more

Use cylindrical shells to find the volume of the solid formed by rotating the region bounded byy = x5+2x, y = 0, x = 0 and x = 1 about the line x=3