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Using differential I want to find the value of the function $g(x,y,z) = \ln \sqrt{x^2+y^2+z^2}$ if we move from (3,4,12) to a distance of 0.1 in the direction of vector $u = 3i+6j-2k$.

I first found $$|u| = \sqrt{9+36+4} = 7$$ so $$u_o = \frac 3 7 i+ \frac 6 7j - \frac 2 7k$$ and $$\nabla g(3,4,12) = \frac 6 {29}i + \frac 8{29}j+ \frac {24}{29}k$$

Then I don't know what to do. Any ideas?

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    Can you explain it a bit more? I think I didn't understand what is going o and that's why I cannot find the solution myself.2012-03-20
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    The change in $g$ is *approximately* the dot product of $\nabla g(3,4,12)$ with $\Delta {\bf x}=.1u_0$. Add the change in $g$ to the "starting value" $g(3,4,12)$.2012-03-20
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    (3,4,12) or(3,4,2)?2012-03-20
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    @Tpofofn Typo. I think it is ok now.2012-03-20

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