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Local Linearity.

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Presentation on theme: "Local Linearity."— Presentation transcript:

1 Local Linearity

2 A nice graph Consider a small portion of the graph . . .

3 “Zooming In” Consider a small portion of the graph . . .
shown here in blue.

4 Zooming Now “zoom in” on the blue part of the graph. . .

5 “Zooming In” And repeat the process by zooming in on the part colored in pink. . .

6 “Zooming In” Keep it up. . .

7 “Zooming In”

8 “Zooming In”

9 “Zooming In”

10 Typical Behavior

11 In general. . . When we zoom in on a “sufficiently nice” function, we see a straight line.

12 Local Linearity

13 Differentiability


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