Mathematics

Problem

To approximate a solution of

y'=y-x^{2}

with

y(0)=0.5

, a student begins with an intended increment of

0.40

. The increment is halved for any step in which

|y'|>1

; otherwise the full increment is used. Using this rule until

x=0.80

is reached, which of the following is the student’s final approximate value for

y

? a) 0.820 b) 1.140 c) 0.916 d) 0.634