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Math Help - linear approximation

  1. #1
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    linear approximation

    1.Find the linear approximation Lo(x) to the function f(x)=sin(x) at x=0
    2.use linear approximation to estimate sin(0.03)
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by bobby77 View Post
    1.Find the linear approximation Lo(x) to the function f(x)=sin(x) at x=0
    I expect you are expecting an answer of the form:

    <br />
Lo(x)=f(0)+x\,f'(0)=0 + x\, \cos(0)=x<br />

    2.use linear approximation to estimate sin(0.03)
    Using the above:

    <br />
\sin(0.03)\approx Lo(0.03)=0.03<br />

    RonL
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  3. #3
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    Quote Originally Posted by bobby77 View Post
    1.Find the linear approximation Lo(x) to the function f(x)=sin(x) at x=0
    2.use linear approximation to estimate sin(0.03)
    The equation of a non-vertical line is passing through point (x_0,y_0) and slope m is,
    \boxed{y-y_0=m(x-x_0)}

    You need to find the equation of tangent line at point (x_0,y_0)=(0,\sin 0)=(0,0).

    And the slope is the derivative at the point,
    \cos x at x=1 yields x=0.

    Thus,
    y-y_0=1(x-0)
    Thus,
    y=x
    Is the linearazation line.

    Thus,
    \sin (.03)\approx .03 (in radians ).
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