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When Tangent Plane = Limit of Secant Plane

Zhibin Yan

Abstract

For function of one variable, differentiability is equivalent to the existence of tangent line as the limit of secant line. The genuine counterpart of this equivalence for function of several variables is obtained for the first time.

When Tangent Plane = Limit of Secant Plane

Abstract

For function of one variable, differentiability is equivalent to the existence of tangent line as the limit of secant line. The genuine counterpart of this equivalence for function of several variables is obtained for the first time.

Paper Structure

This paper contains 1 theorem, 24 equations.

Key Result

Theorem 1

The following two statements are equivalent: If the statements hold, the limit (EqKey) as an explicitly appeared matrix is the total derivative $J$ as an implicitly defined matrix in (EqTotalDiff).

Theorems & Definitions (2)

  • Theorem
  • proof