温州数字教育资源网-温州市教育局-可汗学院：微积分-微分学-0008.夹逼定理

0008.夹逼定理 0.0（0人评）
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00:00:00

Introduction to the Limit Problem

The video begins by introducing the main problem: proving that the limit of sin(x)/x as x approaches zero is equal to one. It also hints that this limit will be proven using an important theorem in calculus.
00:00:44

Introduction to the Squeeze Theorem

This section introduces the Squeeze Theorem (also known as the Sandwich or Pinching Theorem), describing it in simple, intuitive terms through a real-life analogy involving calorie intake.
00:03:06

Formal Definition of the Squeeze Theorem

This section provides a more formal mathematical explanation of the Squeeze Theorem, defining it in terms of functions and limits. It explains how if one function is bounded between two other functions that converge to the same limit, then it must also converge to that limit.
00:04:29

Graphical Representation of the Squeeze Theorem

This part visually illustrates the Squeeze Theorem with a graph. It describes how the middle function is 'squeezed' between the upper and lower bounding functions, which both approach the same limit at a certain point.
00:07:04

Application of the Squeeze Theorem to Prove the Limit

The final section sets up the application of the Squeeze Theorem to prove the main limit of the video: the limit of sin(x)/x as x approaches zero. It emphasizes the importance and usefulness of this limit in calculus and trigonometry.

本视频通过讲解夹逼定理及其应用，逐步引导观众理解并证明当 $ x $ 趋近于 0 时，$ \frac{\sin x}{x} $ 的极限为 1。

课程名称：可汗学院：微积分-微分学

责任教师：管理员单位机构：温州市教育局

课程简介：

姓名	所在单位	学科/专业
管理员	温州市教育局

课程章节
课程资料

自动连播

0001.牛顿，莱布尼茨和尤塞恩·博尔特

0002.极限介绍1

0003.极限介绍2

0004.极限例题1

0005.极限例题2

0006.极限例题3

0007.极限例题4

0008.夹逼定理

0009.证明sinx除以x的极限

0010.更多极限例题

0011.极限的ε-δ定义1

0012.极限的ε-δ定义2

0013.导数(新版本)1

0014.导数(新版本)2

0015.导数(新版本)2.5

0016.直观导数模块

0017.导数1

0018.导数2

0019.导数3

0020.链式法则

0021.链式法则例题

0022.更多链式法则的例题

0023.乘积法则

0024.商法则

0025.导数9

0026.证明：ddx(x^n)

0027.证明：ddx(sqrt(x))

0028.证明：ddx(ln x) = 1x

0029.证明：ddx(e^x) = e^x

0030.证明ln(x)和e^x的导数

0031.31.extreme derivative word problem (advanced)

0032.32.implicit differentiation

0033.33.implicit differentiation (part 2)

0034.34.more implicit differentiation

0035.35.more chain rule and implicit differentiation intuition

0036.36.trig implicit differentiation example

0037.37.calculus derivative of x^(x^x)

0038.38.introduction to l'hopital's rule

0039.39.l'hopital's rule example 1

0040.40.l'hopital's rule example 2

0041.41.l'hopital's rule example 3

0042.42.maxima minima slope intuition

0043.43.inflection points and concavity intuition

0044.44.monotonicity theorem

0045.45.calculus maximum and minimum values on an interval

0046.46.calculus graphing using derivatives

0047.47.calculus graphing with derivatives example

0048.48.graphing with calculus

0049.49.optimization with calculus 1

0050.50.optimization with calculus 2

0051.51.optimization with calculus 3

0052.52.optimization example 4

0053.53.introduction to rate-of-change problems

0054.54.equation of a tangent line

0055.55.rates-of-change (part 2)

0056.56.ladder rate-of-change problem

0057.57mean value theorem

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