A slope field for is drawn on a grid with points spaced unit apart in the –direction

MATHEMATICS · Subjective · AP · Calculus AB · Differential Equations · Differential Equations

Problem

A slope field for

\dfrac{dy}{dx}=y(2-x)

is drawn on a grid with points spaced

0.25

unit apart in the

x

–direction. Beginning at

(0,1)

, follow the tangent segments at

x=0,\,0.25,\,0.50,\,0.75

to approximate the value of

y

when

x=0.75

. Provide your estimate to three decimal places.