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Math Help - Another Linear Approximation Question

  1. #1
    Newbie
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    Another Linear Approximation Question

    I don't even know where to start with this question

    Question:
    A useful linear approximation to
    1/(1+tan x)
    can be obtained by combining the approximations
    1/(1+x) is about equal to 1 - x and tan x is about equal to x
    to get 1/(1+tan x) is about equal to 1-x

    Show that this is the standard linear approximation of 1/(1+ tan x)

    I'm really slow on this linear approximation stuff. Thanks again for helping me out.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Wyau View Post
    I don't even know where to start with this question

    Question:
    A useful linear approximation to
    1/(1+tan x)
    can be obtained by combining the approximations
    1/(1+x) is about equal to 1 - x and tan x is about equal to x
    to get 1/(1+tan x) is about equal to 1-x

    Show that this is the standard linear approximation of 1/(1+ tan x)

    I'm really slow on this linear approximation stuff. Thanks again for helping me out.
    The standard linear approximation of f(x) about x=0 is:

    <br />
f(x) = f(0) + x f'(0)<br />

    So put f(x) = \frac{1}{1+\tan(x)} then you need to show that:

    <br />
f(0)=1<br />

    and:

    <br />
\left[ \frac{df}{dx}\right]_{x=0} = -1<br />

    RonL
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