《微积分 Calculus》课程教学资源（PPT培训课件）Chapter 3 Integration.ppt_大学文库

文档信息

资源类别：文库
文档格式：PPT
文档页数：119
文件大小：3.77MB
团购合买：点击进入团购

内容简介

3.1 Introducing the Derivative 3.2 Rules of Differentiation 3.3 The Product and Quotient Rules 3.4 Derivatives of Trigonometric Functions 3.5 Derivatives as Rates of Change 3.6 The Chain Rule 3.7 Implicit Differentiation 3.8 Derivatives of Logarithmic and Exponential Functions 3.9 Derivatives of Inverse Trigonometric Functions 3.10 Related Rates

刷新页面文档预览

Calculus EARLY TRANSCENDENTALS RIGGs COCHRAN

Chapter 3 Integration PEARSON Copyright @2011 Pearson Education, Inc. Publishing as Pearson Addis on-Wesley

3.1 Introducing the Derivative PEARSON Copyright @2011 Pearson Education, Inc. Publishing as Pearson Addis on-Wesley

O Slope of tangent Slope of tangent line and line and Instantaneous Instantaneous rate of change rate of change are negative are positive FIGURE 3. 1 Copyright@2011 Pearson Education, Inc. Publishing as Pears on Addison-Wesley Slide 3-4

Trajectory of moving object Tangents give direction of motion FIGURE 3.2 Copyright@2011 Pearson Education, Inc. Publishing as Pears on Addison-Wesley Slide 3- 5

slope tan slope m f(r) y=f(r) If()-f(a) a a O lim (x)-f(a) nx→a r-d FIGURE 3.3 Copyright@2011 Pearson Education, Inc. Publishing as Pears on Addison-Wesley Slide 3-6

DEFINITION Rates of Change and the Tangent line The average rate of change in f on the interval [a, x] is the slope of the correspond ing secant line f(r)-f(a) r- a The instantaneous rate of change in f at x= a is f(x-f(a) tan lim x→ax-al which is also the slope of the tangent line at x=a, provided this limit exists. The tangent line at x a is the unique line through(a, f(a)with slope m an. Its equation is y-f(a)= man(x-a) Copyright@2011 Pearson Education, Inc. Publishing as Pears on Addison-Wesley Slide 3-7

y=64x+16 150 16x2+96r 80 (1,80) Slope of tangent 50 line at(1, 80) IS m 64. In FIGURE 3.4 Copyright@2011 Pearson Education, Inc. Publishing as Pears on Addison-Wesley Slide 3-8

slope = mtan sIo sCc f(a+ h f(r) f(a+ h-f( f(a) +h lim f(a+ h)-f(a) tan /→0 h FIGURE 3.5 Copyright@2011 Pearson Education, Inc. Publishing as Pears on Addison-Wesley Slide 3-9

ALTERNATIVE DEFINITION Rates of change and the Tangent Line The average rate of change in f on the interval [a, a+ h] is the slope of the corre sponding secant line f(a+ h-f The instantaneous rate of change inf at x a is f(a+ h-f( man= lim (2) →0 h which is also the slope of the tangent line at x a, provided this limit exists Copyright@2011 Pearson Education, Inc. Publishing as Pears on Addison-Wesley Slide 3-10

共119页，可试读30页，点击继续阅读 ↓

刷新页面下载完整文档

VIP每日下载上限内不扣除下载券和下载次数；
按次数下载不扣除下载券；
注册用户24小时内重复下载只扣除一次；
顺序：VIP每日次数-->可用次数-->下载券；