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 s left parenthesis t right parenthesis equals negative 4.9 t squared plus 15
. Find the instantaneous acceleration of the ball after t seconds.
2.
Find fraction numerator d over denominator d x end fraction left parenthesis 3 over x squared plus x left parenthesis x minus 1 right parenthesis right parenthesis
.
3.
The price p
(in dollars) and the demand x
for an item is given by the price-demand function p left parenthesis x right parenthesis equals 15 minus 0.0015 x
. Find the marginal revenue at x equals 1 comma 000
.
4.
Find the equation of the tangent line to f left parenthesis x right parenthesis equals 3 c s c x plus x sin x
at x equals straight pi over 2
.
5.
A bag of sand hanging from a vertical spring is in simple harmonic motion as given by the position function s left parenthesis t right parenthesis equals negative sin left parenthesis straight pi over 2 t plus straight pi over 6 right parenthesis
where t
is measured in seconds and s
is in inches. Find the velocity of the spring at t equals 2
s.