calculus 1a - 5a

1.

A ball is dropped from the top of a building that is 15 m high. The position of the ball after t seconds is given by the equation . Find the instantaneous acceleration of the ball after t seconds.

2.

Find .

3.

The price (in dollars) and the demand for an item is given by the price-demand function . Find the marginal revenue at .

4.

Find the equation of the tangent line to at .

5.

A bag of sand hanging from a vertical spring is in simple harmonic motion as given by the position function  where is measured in seconds and is in inches. Find the velocity of the spring at s.