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1. . Find the limit: lim ?→ ∞ (? + √?2 + 2?) 2. If 1200...

1. . Find the limit: lim ?→ ∞ (? + √?2 + 2?)

2. If 1200 ??2 of material is available to make a box with a square base and an open top, find the largest possible volume of the box.

2. The volume of a right circular cone is ? =1/3 ??^2 ℎ , where ? is the radius of
the base and ℎ is the height.

(a) Find the rate of change of the volume with respect to the height if the radius is constant.

(b) Fine the rate of change of the volume with respect to the radius if the height is constant.

4. A paper cup has the shape of a cone with height 10 cm and radius 3 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 cm deep?

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milcah answered 2 years ago
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