Question

Use the Euler Method with a step size of 0.2 to estimate f(3) where f′(x)=2x−7 and f(2)=4.

Your answer should be correct to two decimal places.

Answer 1

f(2.2) = f(2) + f'(2) (.2)
f(2.2) = 4 + (2*2-7) (.2)
f(2.2) = 4 + (4-7)(.2)
f(2.2) = 4 + (-3)(.2)
f(2.2) = 3.4

now do f(2.4) the same way
then f(2.6) etc up to f(3)

Answer 2

<img src="http://www.mathscoop.com/image-gallery/slope-fields/2*x-75-55-5ffffff3300661-1120400ff0000240_23190.png " alt="Slope Field by MathScoop.com" />

Answer 3

from
http://www.mathscoop.com/calculus/differential-equations/euler-method-calculator.php

Answer 4

now exact
dy/dx = 2 x - 7
integrate
y = x^2 - 7 x + c
when x = 2, y = 4
4 = 4 -14 + c
c = 14
so
y = x^2 - 7 x + 14
so if x = 3
y = 9 -21 + 14
y = 2 would be exact

Answer 5

If that is the case, Damon, wouldn't the answer just be 1?