Use Euler's method with step size 0.1 to estimate y(2.5), where y(x) is the solution of the initial-value problem y' = 3y + 2xy, y(2) = 1. (Round your answer to four decimal places.) y(2.5) =

1.5939 Correct upto four desimal places

Step-by-step explanation:

To obtain the large value at with small step length and , where we have to use c-programme.  The c-programme for Eular method is given below,

includestdio.h

float funfloat, float

float

return

main

float

printf

scanf

printf

while

printf

which will give required answer , correct upto four desimal places.

  b.   the average rate of change of f(x) is less than the average rate of change of g(x).

step-by-step explanation:

since the length of the interval is the same in each case, we only need to compare the change in y-value to see which is greater.

so the change in y-value for function f is (6 )) = 9.

the table tells us

so the change in y-value for function g is (31 -1) = 30.

the change in y-value of f(x) on the interval is less than the change in y-value of g(x) on the same interval, so the average rate of change of f(x) is less than the average rate of change of g(x).