I got an interesting error message

assume(x>0);
assume(lambda>=0);

f:=(x,lambda)->2/(1+lambda)*1/( 1/(x+lambda)+1/(1+lambda));

                                 2                   
(x, lambda) -> --------------------------------------
                            /    1            1     \
               (1 + lambda) |---------- + ----------|
                            \x + lambda   1 + lambda/

ftilde:=(x,lambda)->1/2*(x+1-(x-1)^2*f(0,lambda)/f(x,lambda));

                                2             
               1     1   (x - 1)  f(0, lambda)
(x, lambda) -> - x + - - ---------------------

with(VectorCalculus):

TangentPlane( x^2+y^2, x=a,y=b);

Error, (in VectorCalculus:-TangentPlane) 2 independent variables 
are required

However this is copied from the Help, last example, (2.8). What wrong in this example? Thanks, Sandor

I have found a very interesting physics problem which describes the motion of an airplane, it is a very simple math model. We use only two coordinates, x(t) and y(t), t is the time. The airplane starts at the point (0,a), a>0 and airport located at the origin (0,0). It leads to the differential system ( v0, w>0 are given ):

sys_ode:=diff(x(t),t)=-v[0]*x(t)/sqrt(x(t)^2+y(t)^2), diff(y(t),t)=-v[0]*y(t)/sqrt(x(t)^2+y(t)^2)+w;

   d                v[0] x(t)         d                v[0] y(t)          
  --- x(t) = - --------------------, --- y(t) = - -------------------- + w
   dt                         (1/2)   dt                         (1/2)    

with(student);
[D, Diff, Doubleint, Int, Limit, Lineint, Product, Sum, Tripleint, changevar, 

  completesquare, distance, equate, integrand, intercept, intparts, leftbox, 

  leftsum, makeproc, middlebox, middlesum, midpoint, powsubs, rightbox, 

  rightsum, showtangent, simpson, slope, summand, trapezoid]
J:=changevar(cos(x)=y,Int(1/(1+a*cos(x)),x=0..Pi/2),y);

                         /1                           
                        |              1              
                        |   ----------------------- dy
                        |                     (1/2)   

Sorry, but I don't understand why Maple produces two different answers. (I make many analysis calculations, some expressions [math functions] come directly, e.g. 5x-3, some by Maple e.g. by series command.)

s:=x-1/2*x^2+1/3*x^3+O(x^4);

                               1  2   1  3    / 4\
                           x - - x  + - x  + O\x /
                               2      3           
t:=series(ln(1+x),x,4);

                               1  2   1  3    / 4\
                           x - - x  + - x  + O\x /
                               2      3           
nops(s);