The discussion focuses on analyzing the function ##\beta(t+\tau)^{-2}e^{-3}cos(at^{3})##, where ##\beta##, ##\tau##, and ##a## are constants. Participants emphasize the importance of identifying benchmarks for accurate graph plotting, particularly at points like ##t = 0## and ##t^3 = \text{multiple of } \pi/a##. The conversation highlights the need to simplify constants to 0 or 1 to better understand the function's behavior, specifically its slope and frequency. Key insights include recognizing the exponential nature of the graph and the significance of cosine frequency in the context of the function.
PREREQUISITESStudents studying calculus, mathematicians analyzing trigonometric functions, and educators seeking to enhance their teaching of graphing techniques.
I have a lot of constant so rather than at ##t=0## the answer says something like slope of about ##\frac{1}{t^2}## and frequency of about ##t^3## how did the get to it?RUber said:Find some benchmarks to plot...i.e. t = 0, ##t^3 =## some multiple of ##\pi/a##.
Once you have some of those magnitudes and periods, you should have all you need.