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Math Help - differentials

  1. #1
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    differentials

    Hi everyone,

    Im having trouble with this problem

    -use differentials to calculate radical 15.4, to 3 correct decimal places.

    -if anyone could help it would be much appreciated
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  2. #2
    Eater of Worlds
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    We can use the formula f(x_{0}+{\Delta}x)\approx{f(x_{0})+f'(x_{0}){\Delt  a}x}

    Let f(x)=\sqrt{x}, \;\ f'(x)=\frac{1}{2\sqrt{x}}

    x_{0}=15, \;\ x_{0}+{\Delta}x=15.4

    We can see then that {\Delta}x=0.4

    f(15.4)=\sqrt{15}+\frac{1}{2\sqrt{15}}(0.4)=3.9246  2312416

    Compare to \sqrt{15.4}=3.92428337407
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  3. #3
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    ok, so for 3 correct decimal places the answer would be 3.925?
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