Barrons AP Calculus

So, if   ,  then    .

(C) The speed,  |v|,    equals   ,  and since   x   =   3y  −   y^2 ,

Then    |v| is  evaluated,  using   y   =   1,  and equals  .

(A) This    is  an  indeterminate   form    of  type     ;  use L’Hôpital’s Rule:

(E) We  find    A   and B   such    that    .

After   multiplying by  the common  denominator,    we  have

3 x +   2   =   A(x −   4)  +   B(x +   3).

Substituting    x   =   −3  yields  A   =   1,  and x   =   4   yields  B   =   2;  hence,

(B) Since   

Then    

Note    that     ,  so  the integral    is  proper.

(D) We  represent   the spiral  as  P(θ)    =   (θ  cos θ,  θ   sin θ). So