Hello and thanks for considering to help me with my problem 
,
So I've gotten the task I wrote below, which is, translated into english:
F be defined as F(x) is defined as the integral from 0 to x for e^-t^2. Calculate the 4th order Taylor-polynom of F with the developmentpoint(?) of x0.
So for the Taylorpolynom I need F(x), F'(x)=f(x), f'(x), f''(x), as its not specifically asked for the error.
What I tried:
F(x)=sqrt(pi)/2 * erf(x), where erf is the error function, which was introduced just today.
F'(x)=e^-t^2 , which I believe is wrong, as F'(x) has x as an argument, and not t, which is what the integral would present.
f'(x)=-2te^-t^2
f''(x)=(-t)^2e^-t^2 + (-2) e^-t^2
T_4=sqrt(pi)/2*erf(0) + e^-0*x + ((-2)*e^(-0^2))/2 * x^2 + ((-2)^2*e^-0^-2)/3! *x^3 = sqrt(pi)/2* 2/sqrt(pi)+x-1/3x^3
Thats my solution, but I don't think I can just form the derivitive this way, as the argument of F(x) is x, and not t.
Would love full solution, but I understand if you prefer to guide me to my solution.
Ruby
, So I've gotten the task I wrote below, which is, translated into english:
F be defined as F(x) is defined as the integral from 0 to x for e^-t^2. Calculate the 4th order Taylor-polynom of F with the developmentpoint(?) of x0.
So for the Taylorpolynom I need F(x), F'(x)=f(x), f'(x), f''(x), as its not specifically asked for the error.
What I tried:
F(x)=sqrt(pi)/2 * erf(x), where erf is the error function, which was introduced just today.
F'(x)=e^-t^2 , which I believe is wrong, as F'(x) has x as an argument, and not t, which is what the integral would present.
f'(x)=-2te^-t^2
f''(x)=(-t)^2e^-t^2 + (-2) e^-t^2
T_4=sqrt(pi)/2*erf(0) + e^-0*x + ((-2)*e^(-0^2))/2 * x^2 + ((-2)^2*e^-0^-2)/3! *x^3 = sqrt(pi)/2* 2/sqrt(pi)+x-1/3x^3
Thats my solution, but I don't think I can just form the derivitive this way, as the argument of F(x) is x, and not t.
Would love full solution, but I understand if you prefer to guide me to my solution.
Ruby
