Posted by **lisa** on Saturday, March 9, 2013 at 2:06pm.

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.

- calculus -
**Damon**, Saturday, March 9, 2013 at 2:36pm
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)

- calculus -
**Damon**, Saturday, March 9, 2013 at 2:41pm
<img src="http://www.mathscoop.com/image-gallery/slope-fields/2*x-75-55-5ffffff3300661-1120400ff0000240_23190.png " alt="Slope Field by MathScoop.com" />

- calculus -
**Damon**, Saturday, March 9, 2013 at 2:42pm
from

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

- calculus -
**Damon**, Saturday, March 9, 2013 at 2:50pm
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

- calculus -
**Nate**, Monday, March 11, 2013 at 1:30am
If that is the case, Damon, wouldn't the answer just be 1?

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