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.

Your answer should be correct to two decimal places.

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

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    posted by Damon
  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

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

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    posted by Nate

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