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onegirl

  • 3 years ago

Find the linear approximation to f(x) at x = x o. Graph the function and its linear approximation. f(x) = sin 3x, x 0, = 0

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  1. onegirl
    • 3 years ago
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    @satellite73 can u help please?

  2. anonymous
    • 3 years ago
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    this is the same as "find the equation of the line tangent to the graph of \(y=\sin(3x)\) at \((0,0)\)"

  3. anonymous
    • 3 years ago
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    take the derivative, replace \(x\) by 0 for the slope (you will get 3) and then use the point slope formula

  4. anonymous
    • 3 years ago
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    since the point is \((0,0)\) the equation of the line will be \(y=3x\)

  5. onegirl
    • 3 years ago
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    ok so find the derivative of sin 3x right?

  6. anonymous
    • 3 years ago
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    yes

  7. onegirl
    • 3 years ago
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    Ok so i got 3cos(3x)

  8. anonymous
    • 3 years ago
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    yes now evaluate at \(x=0\) to find your slope

  9. onegirl
    • 3 years ago
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    ok i got 3

  10. anonymous
    • 3 years ago
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    yes

  11. anonymous
    • 3 years ago
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    that is the slope of your line

  12. onegirl
    • 3 years ago
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    okay so now i have to use the point slop formula?

  13. anonymous
    • 3 years ago
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    yes

  14. anonymous
    • 3 years ago
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    but the point is \((0,0)\) so it is just \(y=3x\)

  15. onegirl
    • 3 years ago
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    okay so what do i do next?

  16. anonymous
    • 3 years ago
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    you are done

  17. onegirl
    • 3 years ago
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    okay

  18. electrokid
    • 3 years ago
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    linear approximation of f(x) at x=x0: \[f(x)=f(x_0)+(x-x_0)f'(x_0)\]

  19. electrokid
    • 3 years ago
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    you can use this way too. (notice the resemblance to equation of line)

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