This preview shows page 1. Sign up to view the full content.
■
Section 3.2
Differentiability (pp. 105–112)
Exploration 1
Zooming in to “See”
Differentiability
1.
Zooming in on the graph of
f
at the point (0, 1) always
produces a graph exactly like the one shown below,
provided that a square window is used. The corner shows
no sign of straightening out.
[
2
0.25, 0.25] by [0.836, 1.164]
2.
Zooming in on the graph of
g
at the point (0, 1) begins to
reveal a smooth turning point. This graph shows the result
of three zooms, each by a factor of 4 horizontally and
vertically, starting with the window
[
2
4, 4] by [
2
1.624, 3.624].
[
2
0.0625, 0.0625] by [0.959, 1.041]
3.
On our grapher, the graph became horizontal after 8 zooms.
Results can vary on different machines.
4.
As we zoom in on the graphs of
f
and
g
together, the
differentiable function gradually straightens out to resemble
its tangent line, while the nondifferentiable function
stubbornly retains its same shape.
[
2
This is the end of the preview. Sign up
to
access the rest of the document.
This note was uploaded on 10/05/2011 for the course MAC 1147 taught by Professor German during the Spring '08 term at University of Florida.
 Spring '08
 GERMAN
 Slope

Click to edit the document details