Barrons AP Calculus

(B) The volume  is  composed    of  elements    of  the form    ΔV  =   (2x)^2  Δy. If  h

is  the depth,  in  feet,   then,   after   t   hr,

(B) Separating  variables   yields

Then

P(t)    =   1000    −   ce−kt.

P(0)    =   300 gives   c   =   700.    P(5)    =   500 yields  500 =   1000    −   700e−^5 k,  so  k

+   0.0673. Now P(10)   =   1000    −   700e−0.673  643.

(C)     arctan  1   =   π.  H′(1)   =   f   (1) =   2.

The equation    of  the tangent line    is  y   −   π   =   2(x −   1).

(C)  Using   midpoint    diameters   to  determine   cylinders,  estimate    the