2-3 積分的意義
【目標】
直觀理解區域面積的基本意義﹐並能透過內接與外接多邊形來估計拋物線下的面 積﹒再者﹐能理解定積分 ∫ a b f x dx ( ) 與函數 f(x)在區間[a﹐b]上可積分的意義﹐並 透過「分割」 、 「上和」 、 「下和」及「數列的極限」求定積分能理解函數可積分與 連續的關係﹐及非負實數值的連續函數其曲線下面積就是 ∫ a b f x dx ( ) ﹐進而理解一 般函數的定積分 ∫ a b f x dx ( ) 與面積的關係﹐認識「微積分基本定理」 、 「反導函數」
The set is the domain of and the corresponding set of values for ( ) is the range of . Example 146 Find the domain of each of the following functions.[r]
Definition 23 The natural logarithmic function is the function that asso- ciates with each positive real number the power to which must be raised to produce .. The function is conti[r]
Chapter 7
Infinite Series
7.1 Sequence
Mathematicslly, a sequence is defined as a function whose domain is the set of positive integrals. Although a sequence is a function, it is common to represent sequence subscript notation rather than by the standard function notation. For instance, in the sequence
In the following pairs, the second series cannot be tested by the same convergence test as the first even thougn it is similar to the first.. (If the ”larger” series[r]
The domain of a function can be descrabed explicitly, or it may be de- scribed implicitly by an equation used to define the function.. The implied domain is the set of all real number fo[r]