Final answer:
To approximate y(1.2) using Taylor's method of order two with h = 0.1, we can use the formula y(x+h) = y(x) + h*y'(x) + (h^2/2)*y''(x). Given that y = 0.011, and y' = y'' = 0, the approximation simplifies to y(1.2) ≈ y(1.1) = 0.011
Step-by-step explanation:
To approximate y(1.2) using Taylor's method of order two with h = 0.1, we can use the formula:
y(x+h) = y(x) + h*y'(x) + (h^2/2)*y''(x)
Given that y = 0.011, we need to find y', y'', and substitute them into the formula.
1. Find y': Take the derivative of y with respect to x, which gives us y' = 0.
2. Find y'': Take the second derivative of y with respect to x, which also gives us y'' = 0.
3. Substitute the values into the formula:
y(1.2) ≈ y(1.1) + 0.1*0 + (0.1^2/2)*0
Simplifying the equation, we find that y(1.2) ≈ y(1.1) = 0.011