Estimate the absolute and relative error of calculating the value of F, if for x 1 , x 2 , x 3 the error Δ = 0.007

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As I understand it, you need to find the absolute error of the exponentiation

step*pow(x,step-1)*absolute_error

in addition / subtraction / multiplication, it is easy to add absolute errors, but what to do with exp( 8* x2 – x1 ) ?

As a result, the absolute error will be obtained, and if you get a number - after substituting x-s, you can find the relative error? Or for functions it does not work?

    1 answer 1

    Generally speaking, usually for F(x) with an error x equal to Δx , the error in the value of the function is ΔF = dF/dx * Δx . For a function of several variables, partial derivatives are taken for each variable, and the errors from different variables, if not mistaken, are summed up as orthogonal — that is, root of the sum of squares.

    As for derivatives, I’m sure about squares - 90% sure :)