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One can zoom in toward a particular point in the domain of a function and see how the graph appears at different zoom levels.

One can zoom in toward a particular point in the domain of a function and see how the graph appears at different zoom levels. For instance, consider the square root function f(x) = V when x is near 2. a. Enter the input below to see the graph of f as x goes from 1 to 3. with(6 = 10), Plot|Vx, (x, 2-6, 2+ 6|| b. Now zoom; change the value of to be 10 and re-enter the input above to see the graph of f as x goes from 1.9 to 2.1. Do this again for 8 = 102, 103, 104, and 10-5. c. Use the last plot to approximate v2 to six significant digits. Check your answer using N. d. When making a Plot, the lower and upper bounds on the iterator must be distinct when rounded to machine precision. Enter the previous Plot command with & = 10-20. An error message results. Read the error message and speculate as to what is happening. The bottom line is that zooming has its limits.

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