Take point B near a certain point A of the curve and make it approach A continuously along the curve. In this way, the limit position of straight line AB is the tangent of the curve at point A ... This is the only definition of tangent in higher mathematics. For example, y = x 3, and the tangent at (0,0) is the straight line y=0. Although there is only one thing in common with the curve, x=0, y=-x and so on. Not its tangent. Another example is y=sinx, and the tangent at (0,0) is y = x.

In function f(x), the value that the function approaches when the independent variable x approaches a certain value infinitely. Maximum: the stagnation point of the maximum and minimum values in a certain range: substitute the value of a certain point of the function into the derivative formula of the function, so that the point with a value of 0 is called the stagnation point of the function.

Extended data:

Tangents and circles have only one common point; The distance between the tangent and the center of the circle is equal to the radius of the circle; The tangent is perpendicular to the radius passing through the tangent point; A straight line passing through the center of the circle and perpendicular to the tangent must pass through the tangent point; The straight line perpendicular to the tangent through the tangent point must pass through the center of the circle; The tangent and secant of a circle drawn from a point outside the circle. The tangent length is the median term of the ratio of the lengths of two lines from this point to the intersection of the secant and the circle.

Among them, the tangent theorem is derived from the definition of tangent, the position relation theorem between straight line and circle and similar triangles. Tangent Theorem: The tangent of a circle is perpendicular to the radius passing through the tangent point. Geometric language: ∵OA is the radius of ⊙O, and the straight line L cuts ⊙O at point A.

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