Pre-Calc Homework Solutions 74

Pre-Calc Homework Solutions 74 - 74 Section 3.2 Quick...

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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
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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.

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