please help! taylor polynominals

Question

Suppose g is a function which has continuous derivatives, and that g(0) = 13, g'(0) = −11, g''(0) = 6and g'''(0) = 9.

1---- What is the Taylor polnomial of degree 2 for g , centered at a=0?

T₂(x)=   

2---- What is the Taylor polnomial of degree 3 for , centered at a=0?

T₃(x)=

3---- Use T₂(x) to approximate g(0.2) ≈

4---- Use T₃(x) to approximate g(0.2) ≈

Answer 1

T₂(x) = g(0) + g'(0) x + (1/2)g''(0) x² = 13 −11x +(1/2) 6 x² = 13 −11x +3 x²

T₂(x) = 13 −11x +3 x²

T₃(x) = g(0) + g'(0) x + (1/2)g''(0) x² + (1/6) g"' (0) x³

T₃(x) = 13 −11x +3 x² + (1/6) g"' (0) x³ = 13 −11x +3 x² +(1/6) 9 x³ = 13 −11x +3 x² +(3/2) x³

T₃(x) = 13 −11x +3 x² +(3/2) x³

T₂(0.2) = 10.92

T₃(0.2) = 10.932