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A nonlinear function f(x) of one variable x can be expanded into an infinite sum of terms of that function’s derivatives evaluated at operating point xo:

(2.1)

xo is the operating point about which the expansion made. Over some range of (x – xo) higher-order terms can be neglected, and the following linear model in the vicinity of the operating point is a sufficiently good approximation of the function:

(2.2)

where

(2.3)

Such an approximation is illustrated in Figure 2.14.

Figure 2.14 Linear approximation of function f(x) at operating point xo.