Barrons AP Calculus

3.

(b)

(c)

4.

Part B

(a) Because  ,  which   never   equals  zero,   the object  is  never   at

rest.

    so  the object’s    speed   is

Position    is  the antiderivative  of  velocity    

Since   P(0)    =   (0,0),  arcsin   + c    =   0,  and thus    c   =   0.

Since       and thus    c   =   2.

Then

Solving x   =   arcsin      for t   yields  t   =   2   sin x.  Therefore

Since   0   ≤ t ≤   1   means   0   ≤ x ≤ , then    cos x > 0,  so  y   =   2   −   2cos    x.

(a)  To  write   the     Maclaurin   series  for    f    (x)     =   ln(e + x),  use     Taylor’s

Theorem at  x   =   0.