Questions from General Calculus

Q: Find the shortest distance from the point (2, 0,

Find the shortest distance from the point (2, 0, -3) to the plane x + y + z = 1.

Q: Find the point on the plane x - 2y + 3z =

Find the point on the plane x - 2y + 3z = 6 that is closest to the point (0, 1, 1).

Q: Find the points on the cone z2 = x2 + y2 that

Find the points on the cone z2 = x2 + y2 that are closest to the point (4, 2, 0).

Q: Find the points on the surface y2 = 9 + xz that

Find the points on the surface y2 = 9 + xz that are closest to the origin.

Q: Find three positive numbers whose sum is 100 and whose product is

Find three positive numbers whose sum is 100 and whose product is a maximum.

Q: Find three positive numbers whose sum is 12 and the sum of

Find three positive numbers whose sum is 12 and the sum of whose squares is as small as possible.

Q: Find the maximum volume of a rectangular box that is inscribed in

Find the maximum volume of a rectangular box that is inscribed in a sphere of radius r.

Q: Find the dimensions of the box with volume 1000 cm3 that has

Find the dimensions of the box with volume 1000 cm3 that has minimal surface area.

Q: One side of a triangle is increasing at a rate of 3

One side of a triangle is increasing at a rate of 3 cm/s and a second side is decreasing at a rate of 2 cm/s. If the area of the triangle remains constant, at what rate does the angle between the side...

Q: Level curves for barometric pressure (in millibars) are shown for

Level curves for barometric pressure (in millibars) are shown for 6:00 am on a day in November. A deep low with pressure 972 mb is moving over northeast Iowa. The distance along the red line from K (K...