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anonymous

  • one year ago

If the local linear approximation of f(x) = 2cos x + e2x at x = 2 is used to find the approximation for f(2.1), then the % error of this approximation is greater than 15% between 11% and 15% between 5% and 10% between 0% and 4

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  1. anonymous
    • one year ago
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    @jim_thompson5910

  2. jim_thompson5910
    • one year ago
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    how far did you get here?

  3. anonymous
    • one year ago
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    well i found the linear approximation for f(2.1) using x = 2

  4. jim_thompson5910
    • one year ago
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    what did you get for f ' (x)

  5. anonymous
    • one year ago
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    tell me if i did thi right f(2.1) = 53.76 + 107.38(x - 2) f(2.1) = 107.38x - 161

  6. jim_thompson5910
    • one year ago
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    I'm getting y = 107.37771x - 160.98955 for the tangent line

  7. jim_thompson5910
    • one year ago
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    let g(x) = 107.37771x - 160.98955 compute g(2.1) and compare that with f(2.1)

  8. anonymous
    • one year ago
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    g(2.1) = 64.503641 f(2.1) = 65.67663883

  9. jim_thompson5910
    • one year ago
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    now compute the percent error using those f(2.1) and g(2.1) values

  10. anonymous
    • one year ago
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    so just divide them by each other?

  11. jim_thompson5910
    • one year ago
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    \[\Large \text{Percent Error} = \frac{|\text{Approximate Value}-\text{Exact Value}|}{\text{Exact Value}}\] \[\Large \text{Percent Error} = \frac{|g(2.1)-f(2.1)|}{f(2.1)}\] \[\Large \text{Percent Error} = ??\]

  12. anonymous
    • one year ago
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    1.81

  13. anonymous
    • one year ago
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    are you sure it's not backwards on the numerator

  14. anonymous
    • one year ago
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  15. jim_thompson5910
    • one year ago
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    the order in the numerator does not matter because |x - y| = |y - x|

  16. jim_thompson5910
    • one year ago
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    if the absolute value bars weren't there, then yeah, the order matters

  17. anonymous
    • one year ago
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    okay well thank you very much :D!!!

  18. jim_thompson5910
    • one year ago
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    I'm getting roughly 0.01786 which is approximately 1.786% error

  19. anonymous
    • one year ago
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    yeah me too either way its D

  20. jim_thompson5910
    • one year ago
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    yes

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