用導(dǎo)數(shù)的定義求極限(limit)_AP 微積分
DEFINITION OF DERIVATIVE ( 導(dǎo)數(shù)的定義）
The fraction?? is called the difference quotient for
at
?and represents the average rate of change (ARC) of
? from a to a + h.?
Geometrically, it is the slope of the secant PQ to the curve y = f(x) through the points P(a, f(a)) and Q(a + h, f(a + h)). The limit, f′(a), of the difference quotient is the (instantaneous) rate of change of f at point a. Geometrically (see Figure 3–1a), the derivative f′(a) is the limit of the slope of secant PQ as Q approaches P—that is, as h approaches zero. This limit is the slope of the curve at P. The tangent to the curve at P is the line through P with this slope.
在幾何學(xué)上，它是通過點(diǎn)P(a, f(a))和Q(a+h, f(a+h))的曲線y=f(x)的割線PQ的斜率。? ? ? ? ? ? ? ? ?差商的極限f′(a)是在a點(diǎn)的（瞬時）變化率。這個極限就是曲線在P點(diǎn)的斜率，曲線在P點(diǎn)的切線就是通過P點(diǎn)的斜率的直線。
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