A student uses a tangent-line approximation with constant step size to estimate the…
MATHEMATICS · Single correct · AP · Calculus BC · Differential Equations · Differential Equations
Problem
A student uses a tangent-line approximation with constant step size h to estimate the value of y at x=b for a solution of the differential equation dxdy=f(x,y) on the interval [a,b]. Which of the following adjustments is MOST likely to decrease the overall absolute error of the estimate without introducing additional correction techniques?
(a) Keep the same step size h but evaluate the slope at the midpoint of each subinterval.
(b) Halve the step size h and take twice as many steps across [a,b].
(c) Double the step size h so the approximation reaches b in fewer steps.
(d) Keep the same step size h but begin the approximation at a point closer to b.