Congratulations Andrei for another very good solution.

The 4 functions are:
A(x) = sinx,    B(x) = 1 - cosx,    C(x) = log(1+x),     D(x) = 1- 1
(1-x)
 .
I consider the logarithm in base e. First I plotted the 4 functions using Graphmatica. In all figures A(x) is violet, B(x) is white, C(x) is red and D(x) is cyan. For [-1, 1] I obtain:
graphs for tiny x

For [-0.1, 0.1]
graphs for -.1 to .1


And for [-0.01, 0.01] I have:
graphs for -.01 to .01
Each of the 4 functions could be approximated using the Taylor series expansion around 0, and the accuracy of the approximation becomes better for values of x nearer to the origin. I shall use the second order polynomial:
A(x) » x,    B(x) » 1- (1 - x2/2) = x2/2,     C(x) » x - x2/2,     D(x) » - x - x2.