Use Taylor’s theorem, retaining powers of x − x0 sufficiently large to approximate the values of y accurately to two decimal places on the given interval using the prescribed increments in x. In Exercises 1 through 6, compare the estimated values with the correct values obtained by solving the problem exactly using elementary methods.
y′ = x + y; whenx = 2, y = − 1;Δx = 0.1 and 2 ≤ x ≤3.
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