Barrons AP Calculus

(B)

(D) Evaluate    .

(A)     at  the point   (3, 4).

Use,    also,   the facts   that    the speed   is  given   by      and that    the

point    moves   counterclockwise;   then    ,   yielding    and    

    at  the given   point.  The velocity    vector, v,  at  (3, 4)  must    therefore

be  .

(A)

(B) The formula for length  of  arc is

Since   y   =   2x, we  find

(D) a(t)    =   (0, et);    the acceleration    is  always  upward.

(A) At   ,  so  Euler’s method  yields  (0.1,   1   +   0.1(4)) =   (0.1,   1.4).

    has particular  solution    y   =   e^4 x   ;   the error   is  e4(0.1) −   1.4.