Barrons AP Calculus

(E) Separating  variables,  we  get y   dy  =   (1  −   2x) dx. Integrating gives

or

y^2     =   2x  −   2x^2    +   k

or

2 x^2   +   y^2     −   2x  =   k.

(E)

(E)

(D) Use L’Hôpital’s Rule    or  rewrite the expression  as  

(D) For f   (x) =   tan x,  this    is  .

(E) The parameter   k   determines  the amplitude   of  the sine    curve.  For f   =   k

sin x   and g   =   ex  to  have    a   common  point   of  tangency,   say at  x   =   q,  the

curves  must    both    go  through (q, y)  and their   slopes  must    be  equal   at  q.