Barrons AP Calculus

.

(c)     means   1   +   4   ·   2−t =   1.25,   so  t   =   4.

(d) ,   so  the value   of  y   approaches  10.

(a) Since    .  Since   y   =   18  −   2   ·   2^2     =   10, P   is  at  (2,10).

(b) Since    .  Since    .  Therefore

    unit/sec.

(c) Let D   =   the object’s    distance    from    the origin. Then

(d) The object  hits    the x-axis  when    y   =   18  −   2x^2    =   0,  or  x   =   3.  Since   

.

(e) The length  of  the arc of  y   =   18  −   2x^2    for 0   ≤   x   ≤   3   is  given   by

    units.

(a) See graph.