Let f(x)=sqrt(x+1);Compute T1,T2 at 0. And by that I mean Taylor . I know how to compute a Taylor polynomial for f(x,y) but how do I compute for f(x)?

Question

Let f(x)=sqrt(x+1);

Compute T1,T2 at 0. And by that I mean Taylor .

I know how to compute a Taylor polynomial for f(x,y) but how do I compute for f(x)?

 

Please help I have an exam tomorrow :( ...

Answer 1

f(x) = √(x+1)   f'(x) = (1/2)(x+1)^-½   f"(x) = (-¼)(x+1)^-3/2

 

T₁(x) = f(0) + [f'(0)/1!](x-0)¹ = 1 + (½)x

 

T₂(x) = f(0) + [f'(0)/1!](x-0)¹ + [f"(0)/2!](x-0)² = 1 + (½)x - (1/8)x²