Taylor Approximation

Question

f(x) = Square root(X+6)

The third-order Taylor approximation at the point x=0 is (round answers to three decimal points):

___+____x+_____x²+____x³

Answer 1

f(0) = √6 ≈ 2.449; f'(x) = 1/2(x + 6)^-1/2; f'(0) = 1/(2√6) ≈ 0.204; f''(x) = -1/4(x + 6)^-3/2; f''(0) = -1/(4√6³) ≈ - 0.017.

f'''(x) = 3/8(x + 6)^-5/2; f''(0) = 3/(8·6^5/2) ≈ 0.004

So; √(x + 6) ≈ 2.449 + 0.204x - 0.009x² + 0.0007x³...