Fun with graphs and calculators

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SUMMARY

This discussion emphasizes the importance of understanding mathematical concepts in calculus rather than solely relying on graphing calculators like the TI-83 and TI-84. The user successfully demonstrated the graph of sin(15*pi*x) using two different window sizes: xmin=-2pi to xmax=2pi and xmin=-6.1 to xmax=6. The results highlight that the choice of window size significantly affects the representation of the function, prompting a discussion on the implications of these choices. The use of Wolfram Alpha is recommended for further analysis.

PREREQUISITES
  • Understanding of calculus concepts, particularly functions and integrals.
  • Familiarity with graphing calculators, specifically TI-83 and TI-84 models.
  • Basic knowledge of trigonometric functions, especially sine functions.
  • Experience with interpreting graphical data and window settings in graphing tools.
NEXT STEPS
  • Explore the capabilities of the TI-89 graphing calculator for advanced graphing techniques.
  • Learn how to effectively use Wolfram Alpha for mathematical graphing and analysis.
  • Research the impact of window size on graph representation in various graphing calculators.
  • Study the principles of function periodicity and its visual implications in graphing.
USEFUL FOR

Students, educators, and anyone interested in enhancing their understanding of calculus and graphing techniques, particularly those using graphing calculators for mathematical functions.

Office_Shredder
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I was coming up with examples for my students as to why we demand they actually understand math in calculus class instead of plugging all their functions into their graphing calculators to draw graphs and calculate integrals. I basically hit the motherload... I have confirmed this works on TI-83 and TI-84, so I imagine it works for TI-89s as well. Other graphing calculators probably require a different period depending on the screen size(if you have one post here and let us know what works!)

Draw the graph of sin(15*pi*x) with two different choices for the window size. For the first choice, let xmin=-2pi and xmax=2pi. For the second time, let xmin=-6.1 and xmax=6

Which graph is a worse representation of the function? Discuss.
 
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