# List of functions used for infinitesimal approaching.
# An item in this list will be picked randomly at each exercise.
# Structure of item: multi-line.
# line 1 is function description.
# line 2 is x_0.
# line 3 is order function.
# The rest is values for parameters c1, c2, etc.
# Different items are separated by lines starting with `:'.

:a1/(1+c2)+a2/(2+c2),a3/(3+c2)+c1
 1,2,3,4,5
 o
 e^x,2^x,ln(1+x),sin(x),cos(x),x,2*x,3*x,-x,-2*x,-3*x,1,2,3,4,5,-1,-2,-3,-4,-5
 x,x^2,x+x^2,-x+x^2
:a1*cos(x)+a2*sin(x),a3*e^x+c1+c2
 -3,-2,-1,1,2,3
 o
 -9,-8,-7,-6,-5,-4,-3,-2,-1,1,2,3,4,5,6,7,8,9
 ln(1+x^2),-3*x,-2*x,-x,x,2*x,3*x,2^x,-2*x,x+x^2,x-x^2,-x+x^2,-x-x^2
:a1*exp(x)+a2*exp(-x)+a3*exp(c1*x),c2*c3
 -3,-2,-1,0,1,2,3
 o
 -3,-2,2,3
 -9,-8,-7,-6,-5,-4,-3,-2,2,3,4,5,6,7,8,9
 2^x,ln(1+x^2),sin(x),cos(x),x,x^2,x^3,(x^2+x),(x^2-x),arctg(x)
:a1*c1(x)+a2*c1(2*x)+a3*c1(3*x),c3+c2
 -5,-4,-3,-2,-1,0,1,2,3,4,5
 o
 sin,cos,arctg,Argsh
 -9,-8,-7,-6,-5,-4,-3,-2,2,3,4,5,6,7,8,9
 2^x,ln(1+x^2),x,x^2,x^3,x^2+x,x^2-x,-x,-x^2,-x^3,-x^2+x,-x^2-x,1/(x^2+1),1/(x^2+x+1)
:a1*2^x+a2*3^x+a3*4^x,c1+c2*c3
 -2,-1,0,1,2
 o
 -9,-8,-7,-6,-5,-4,-3,-2,-1,1,2,3,4,5,6,7,8,9
 -9,-8,-7,-6,-5,-4,-3,-2,2,3,4,5,6,7,8,9
 e^x,ln(1+x^2),sin(x),cos(x),x,x^2,x^3,(x^2+x),(x^2-x),arctg(x)
 
