Approximations of for the differential equation with are listed below

MATHEMATICS · Subjective · AP · Calculus BC · Differential Equations · Differential Equations

Problem

Approximations of

y(0.4)

for the differential equation

\dfrac{dy}{dx}=x+y

with

y(0)=1

are listed below. h \ (units) | Approximation of

y(0.4)

0.20 | 1.480 0.10 | 1.492 0.05 | 1.4920 The exact value is 1.4918 (rounded). Identify the smallest step size

h

from the table that keeps the absolute error below 0.001.