a ladder 4m long at a construction site is resting against a wall the bottom of the ladder is slipping away from the wall find the estimate of the instantaneous rate of change of the height of the top of the ladder with respect to distance pf the bottom of the ladder from the wall when the bottom of the ladder is 2.5m away from the wall ise h=0.01 and the central interval

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An ant colony explores an area enclosed by a circle centered at its nest. This area (and the circle containing it) expands as they have time to explore. Due to the need for ants to return to the colony periodically, as the radius expands, the change in the radius of the area explored with respect to time slows down. Specifically, if r is the radius of the area the ants have explored in meters, then = 3 m/day. Find the rate of change of the area explored by the ants 4 in m2/day when the radius of the area explored is 3m. dt

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