When using equal-length tangent segments taken from a slope field to estimate a…
MATHEMATICS · Single correct · AP · Calculus AB · Differential Equations · Differential Equations
Problem
When using equal-length tangent segments taken from a slope field to estimate a solution curve, which statement best describes how decreasing the step size Δx affects the estimate?
(a) The estimate becomes less accurate because rounding error from the many small steps dominates.
(b) The estimate becomes less accurate because the errors from each additional segment accumulate.
(c) The estimate generally becomes more accurate because the local linearity error decreases.
(d) The estimate is unchanged since each tangent segment already gives the exact slope information.