Can someone please help me figure out this problem dealing with taylor series?

Question

find the taylor polynomial Tsubn (x) for the function f at the number a.
f(x)= square root of quantity (3+x^2), a=1, n=2

my teacher said to compute the taylor polynomial. i'm not sure what that means

Answer 1

f(x) = sqrt(3+x^2)
f¨(x) 1/sqrt(3+x^2)* x
f(x) =2 +(x-1) /2 = x/2+3/2 (two terms)

Answer 2

y --> y(0)=-a million y' --> y'(0)=a million y''= x+y-y² --> y''(0)= 0-a million-(-a million)² =-2 y'''=a million+y'-2·y·y' --> y'''(0)= a million+a million-2·(-a million)·a million=4 y''''=y'' -2·(y'·y' +y·y'') = y'' -2·y·y'' - 2·(y')² --> y''''(0)= (-2)-2·(-a million)·(-2) -2 ·a million² = -2-4-2= -8 y'''''= y''' -2·(y'·y''+y·y''') - 2·2·y' · y'' = y''' - 2·y'·y'' - 2·y·y''' -4·y'·y'' = y''' -2·y·y''' -6·y'·y'' --> y'''''(0)= 4-2·(-a million)·4 -6·a million·(-2) = 4 +8 + 12 = 24 y~ -a million+ x - x² + 2/3· x³ - a million/3· x^4... (the 1st 5 non-0 words ) y~-a million+ x - x² + 2/3· x³ - a million/3· x^4+ a million/5· x^5 (the 1st 6 non-0 words) -..... Saludos