1. . Find the limit: lim ?→ ∞ (? + √?2 + 2?)
2. If 1200 ??2 of material is available to make a box with a squarebase and an open top, find the largest possible volume of thebox.
2. The volume of a right circular cone is ? =1/3 ??^2 â„Ž , where ?is the radius of
the base and â„Ž is the height.
(a) Find the rate of change of the volume with respect to theheight if the radius is constant.
(b) Fine the rate of change of the volume with respect to theradius if the height is constant.
4. A paper cup has the shape of a cone with height 10 cm and radius3 cm (at the top). If water is poured into the cup at a rate of 2??3/?, how fast is the water level rising when the water is 5 cmdeep?
