chapter 4 – applications of derivatives
TRANSCRIPT
![Page 1: Chapter 4 – Applications of Derivatives](https://reader031.vdocument.in/reader031/viewer/2022012016/615a9eb110ddd43ca1719cc2/html5/thumbnails/1.jpg)
Partial DerivativesChapter 1
1
![Page 2: Chapter 4 – Applications of Derivatives](https://reader031.vdocument.in/reader031/viewer/2022012016/615a9eb110ddd43ca1719cc2/html5/thumbnails/2.jpg)
Cylinders and Quadric SurfacesSection A
2
![Page 3: Chapter 4 – Applications of Derivatives](https://reader031.vdocument.in/reader031/viewer/2022012016/615a9eb110ddd43ca1719cc2/html5/thumbnails/3.jpg)
Cylinders
3
![Page 4: Chapter 4 – Applications of Derivatives](https://reader031.vdocument.in/reader031/viewer/2022012016/615a9eb110ddd43ca1719cc2/html5/thumbnails/4.jpg)
Cylinders
4
![Page 5: Chapter 4 – Applications of Derivatives](https://reader031.vdocument.in/reader031/viewer/2022012016/615a9eb110ddd43ca1719cc2/html5/thumbnails/5.jpg)
5
![Page 6: Chapter 4 – Applications of Derivatives](https://reader031.vdocument.in/reader031/viewer/2022012016/615a9eb110ddd43ca1719cc2/html5/thumbnails/6.jpg)
6
![Page 7: Chapter 4 – Applications of Derivatives](https://reader031.vdocument.in/reader031/viewer/2022012016/615a9eb110ddd43ca1719cc2/html5/thumbnails/7.jpg)
7
![Page 8: Chapter 4 – Applications of Derivatives](https://reader031.vdocument.in/reader031/viewer/2022012016/615a9eb110ddd43ca1719cc2/html5/thumbnails/8.jpg)
8
![Page 9: Chapter 4 – Applications of Derivatives](https://reader031.vdocument.in/reader031/viewer/2022012016/615a9eb110ddd43ca1719cc2/html5/thumbnails/9.jpg)
9
![Page 10: Chapter 4 – Applications of Derivatives](https://reader031.vdocument.in/reader031/viewer/2022012016/615a9eb110ddd43ca1719cc2/html5/thumbnails/10.jpg)
10
![Page 11: Chapter 4 – Applications of Derivatives](https://reader031.vdocument.in/reader031/viewer/2022012016/615a9eb110ddd43ca1719cc2/html5/thumbnails/11.jpg)
11
![Page 12: Chapter 4 – Applications of Derivatives](https://reader031.vdocument.in/reader031/viewer/2022012016/615a9eb110ddd43ca1719cc2/html5/thumbnails/12.jpg)
12
![Page 13: Chapter 4 – Applications of Derivatives](https://reader031.vdocument.in/reader031/viewer/2022012016/615a9eb110ddd43ca1719cc2/html5/thumbnails/13.jpg)
Functions of Several VariablesSection B
13
![Page 14: Chapter 4 – Applications of Derivatives](https://reader031.vdocument.in/reader031/viewer/2022012016/615a9eb110ddd43ca1719cc2/html5/thumbnails/14.jpg)
14
![Page 15: Chapter 4 – Applications of Derivatives](https://reader031.vdocument.in/reader031/viewer/2022012016/615a9eb110ddd43ca1719cc2/html5/thumbnails/15.jpg)
What about domains and ranges?
15
![Page 16: Chapter 4 – Applications of Derivatives](https://reader031.vdocument.in/reader031/viewer/2022012016/615a9eb110ddd43ca1719cc2/html5/thumbnails/16.jpg)
Definitions
16
![Page 17: Chapter 4 – Applications of Derivatives](https://reader031.vdocument.in/reader031/viewer/2022012016/615a9eb110ddd43ca1719cc2/html5/thumbnails/17.jpg)
Definitions
17
![Page 18: Chapter 4 – Applications of Derivatives](https://reader031.vdocument.in/reader031/viewer/2022012016/615a9eb110ddd43ca1719cc2/html5/thumbnails/18.jpg)
Definitions
18
![Page 19: Chapter 4 – Applications of Derivatives](https://reader031.vdocument.in/reader031/viewer/2022012016/615a9eb110ddd43ca1719cc2/html5/thumbnails/19.jpg)
Level curves
19
![Page 20: Chapter 4 – Applications of Derivatives](https://reader031.vdocument.in/reader031/viewer/2022012016/615a9eb110ddd43ca1719cc2/html5/thumbnails/20.jpg)
Level curves
20
![Page 21: Chapter 4 – Applications of Derivatives](https://reader031.vdocument.in/reader031/viewer/2022012016/615a9eb110ddd43ca1719cc2/html5/thumbnails/21.jpg)
Contour curves
21
![Page 22: Chapter 4 – Applications of Derivatives](https://reader031.vdocument.in/reader031/viewer/2022012016/615a9eb110ddd43ca1719cc2/html5/thumbnails/22.jpg)
Contour curves
22
![Page 23: Chapter 4 – Applications of Derivatives](https://reader031.vdocument.in/reader031/viewer/2022012016/615a9eb110ddd43ca1719cc2/html5/thumbnails/23.jpg)
Level surface
23
![Page 24: Chapter 4 – Applications of Derivatives](https://reader031.vdocument.in/reader031/viewer/2022012016/615a9eb110ddd43ca1719cc2/html5/thumbnails/24.jpg)
Level surface
24
![Page 25: Chapter 4 – Applications of Derivatives](https://reader031.vdocument.in/reader031/viewer/2022012016/615a9eb110ddd43ca1719cc2/html5/thumbnails/25.jpg)
Definitions
25
![Page 26: Chapter 4 – Applications of Derivatives](https://reader031.vdocument.in/reader031/viewer/2022012016/615a9eb110ddd43ca1719cc2/html5/thumbnails/26.jpg)
Computer graphing
26
![Page 27: Chapter 4 – Applications of Derivatives](https://reader031.vdocument.in/reader031/viewer/2022012016/615a9eb110ddd43ca1719cc2/html5/thumbnails/27.jpg)
Computer graphing
27
![Page 28: Chapter 4 – Applications of Derivatives](https://reader031.vdocument.in/reader031/viewer/2022012016/615a9eb110ddd43ca1719cc2/html5/thumbnails/28.jpg)
Computer graphing
28
![Page 29: Chapter 4 – Applications of Derivatives](https://reader031.vdocument.in/reader031/viewer/2022012016/615a9eb110ddd43ca1719cc2/html5/thumbnails/29.jpg)
Computer graphing
29
![Page 30: Chapter 4 – Applications of Derivatives](https://reader031.vdocument.in/reader031/viewer/2022012016/615a9eb110ddd43ca1719cc2/html5/thumbnails/30.jpg)
Computer graphing
30
![Page 31: Chapter 4 – Applications of Derivatives](https://reader031.vdocument.in/reader031/viewer/2022012016/615a9eb110ddd43ca1719cc2/html5/thumbnails/31.jpg)
Limits and ContinuitySection C
31
![Page 32: Chapter 4 – Applications of Derivatives](https://reader031.vdocument.in/reader031/viewer/2022012016/615a9eb110ddd43ca1719cc2/html5/thumbnails/32.jpg)
Informal definition of the limit
32
![Page 33: Chapter 4 – Applications of Derivatives](https://reader031.vdocument.in/reader031/viewer/2022012016/615a9eb110ddd43ca1719cc2/html5/thumbnails/33.jpg)
Formal definition of the limit
33
![Page 34: Chapter 4 – Applications of Derivatives](https://reader031.vdocument.in/reader031/viewer/2022012016/615a9eb110ddd43ca1719cc2/html5/thumbnails/34.jpg)
Formal definition of the limit
34
![Page 35: Chapter 4 – Applications of Derivatives](https://reader031.vdocument.in/reader031/viewer/2022012016/615a9eb110ddd43ca1719cc2/html5/thumbnails/35.jpg)
Formal definition of the limit
35
![Page 36: Chapter 4 – Applications of Derivatives](https://reader031.vdocument.in/reader031/viewer/2022012016/615a9eb110ddd43ca1719cc2/html5/thumbnails/36.jpg)
Properties of limits
36
![Page 37: Chapter 4 – Applications of Derivatives](https://reader031.vdocument.in/reader031/viewer/2022012016/615a9eb110ddd43ca1719cc2/html5/thumbnails/37.jpg)
37
![Page 38: Chapter 4 – Applications of Derivatives](https://reader031.vdocument.in/reader031/viewer/2022012016/615a9eb110ddd43ca1719cc2/html5/thumbnails/38.jpg)
Continuity
38
![Page 39: Chapter 4 – Applications of Derivatives](https://reader031.vdocument.in/reader031/viewer/2022012016/615a9eb110ddd43ca1719cc2/html5/thumbnails/39.jpg)
39
![Page 40: Chapter 4 – Applications of Derivatives](https://reader031.vdocument.in/reader031/viewer/2022012016/615a9eb110ddd43ca1719cc2/html5/thumbnails/40.jpg)
Two-path test for nonexistence of a limit
40
![Page 41: Chapter 4 – Applications of Derivatives](https://reader031.vdocument.in/reader031/viewer/2022012016/615a9eb110ddd43ca1719cc2/html5/thumbnails/41.jpg)
41