Barrons AP Calculus

(B) ,   so  v   =   3t^3    +   c.

Since   v   =   1   when    t   =   0,  c   =   1.

Now  ,  so  s   =   t^3     +   t   +   c.

Since   s   =   3   when    t   =   0, c    =   3;  then    s   =   t^3     +   t   +   3.

(A) Let u   =   x^2 .   Then

(C)

To  find    a,  the point   of  intersection    of  y   =   x^2     and y   =   cos (x),    use your

calculator  to  solve   the equation    x^2     −   cos (x) =   0.  (Store  the value   for later

use;    a   ≈   0.8241.)

As  shown   in  the diagram above,  ΔA  =   (cos    (x) −   x^2 )Δx.

Evaluate    the area:   .

(D) If  x   =   2t  +   1,  then     ,  so   .  When    t   =   0,  x   =   1;  when    t   =   3,

x   =   7.