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University of North Texas

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Problem 23 Easy Difficulty

Graph the function using as many viewing rectangles as you need to depict the true nature of the function.

$ f(x) = \dfrac{1 - \cos(x^4)}{x^8} $

Answer

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Video Transcript

we want to crack the function if Alexis is equal to one minus co sign of excellent one over X A using as many viewing rectangles as we need to depict the true nature of the auction. So this first graph that we have here kind of in the center is just what I got when I kind of zoom function out a little bit and we could see that around here. It looks like we have a local for some local. Max is down here. We have some local men's, so we may want to zoom into this region. A lot of it, and we can also see in these two regions hero on the side. It looks like it has this kind of periodic pattern to it that dampens as we go to infinity. And so first, let's go ahead and zoom in to Let's just do the left hand side and doing that gives us this craft here, so it kind of looks like sign or co signed. But adjusted dampens over time, and it just keeps getting closer and closer to zero. And for this middle region right here, I went ahead and zoomed into around there. And you can see that as we get closer to X is equal to zero. It just looks like it starts the oscillator a lot more and more. And then I kept trying to zoom in more and more on the graphic a clue that I have. And it really never showed what happened in this region here. So you might I want to say that nothing of interest really happens here. Maybe he goes in your negative infinity. Uh, but if you burn too, actually look at the limit as expertise a row of this it should go to one. So you had a better graphing calculator that was able to go to more precise values. It should keep getting closer and closer and get closer to 1/2. But at least a graphing calculator that I have here wasn't really showing that so. But I think these three viewing with those overall describes at least the best abilities of what I can show of the overall nature of this graph.