When a variable X tends to a value A more and more, the process of this trend will go on endlessly, and the difference between X and A will infinitely tend to 0, so that A is the limit of X. This difference is called "infinitesimal", which is a process of getting smaller and smaller, and it is a process of infinitely tending to 0, and it is not a small number, but a process of tending to 0.
If the gap between x 1 and x2 is small, the small is limited. When the gap between x 1 and x2 decreases infinitely and approaches infinitely, the gap between x 1 and x2 approaches to zero infinitely in the process of approaching. At this time, it is written as dx, that is, δx is a finite quantity.
Dx is an infinitesimal quantity.
Geometric significance of extended data differentiation
Let Δ x be the increment of point m on the curve on the abscissa y = f(x), Δ y be the increment of the curve on point m corresponding to Δ x on the ordinate, and dy be the increment of the tangent of the curve on point m corresponding to Δ x on the ordinate. F'(x0) is the slope of the tangent of the curve y=f(x) at the tangent point M(x0, f(x0)). When | Δ x | is very small, |Δy-dy | is much smaller than |δx | (high-order infinitesimal), so the curve segment can be approximately replaced by a tangent segment near point m.
According to the oblique equation of straight line points, the tangent equation is: y-y0=f'(x0)(x-x0), the product of the slopes of two mutually perpendicular straight lines is-1, and the tangent is perpendicular to the normal, so the normal equation is: y-y0 =-1/f' (x0) * (.
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