To approximate the solution of with

MATHEMATICS · Single correct · AP · Calculus BC · Differential Equations · Differential Equations

Problem

To approximate the solution of

\displaystyle \frac{dy}{dx}=x^{2}-y

with

y(0)=0.5

, a student proceeds from

x=0

x=0.25

in three stages: • first increment

\Delta x=0.10

(from

0

0.10

) • second increment

\Delta x=0.10

(to

0.20

) • third increment

\Delta x=0.05

(to

0.25

) Each time the student updates

y

using the derivative evaluated at the left end of the subinterval. What value does the student obtain for

y(0.25)

? (a)

0.392

(b)

0.406

(c)

0.388

(d)

0.369