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 .