# calculus

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

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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)

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posted by Damon
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" />

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posted by Damon
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posted by Damon
3. 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

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posted by Damon
4. If that is the case, Damon, wouldn't the answer just be 1?

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posted by Nate

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