Omnimaga
Calculator Community => Other Calculators => Topic started by: piexil on March 23, 2013, 12:07:28 pm
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One day, while bored in AP chemistry, I decided to just start randomly graphing things.
I started with the function f(x)=x^(sin(x)), now this graphs pretty normally on the 83/84, but on the nspire, it goes crazy while in 2D graphing mode
(http://i.imgur.com/JozxT6g.png)
So I graphed i in 3d mode to see what would happen, and it comes out as it should
(http://i.imgur.com/0Nw1JxP.png)
Hmm, I wonder if any other functions cause this too happen, and I discovered another weird one with
f(x)=x^x^x^2
2d: (http://i.imgur.com/kB66jr7.png)
3d: (http://i.imgur.com/HAQBMJJ.png)
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What I think is happening here is a problem with calculating. I don't know what the Nspire does exactly when plotting, but I think it makes a taylor expansion to fit the function. The taylor expansion of x^sin(x) at x=0 looks like 1+x*ln(x)+0.5*x²*ln²(x). Therefore entering negative values for x results in a calculation error. The same goes for x^x^x^2, which has a taylor expansion of x+x^3 log^2(x)+O(x^4). Probably a lot of other functions have this problem as well.
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Doesn't really answer to the topic, but piexil, you can use [img] tags to include the image in your post without users having to click on it ;)
For example, [img]http://i.imgur.com/0Nw1JxP.png[/img] gives that:
(http://i.imgur.com/0Nw1JxP.png)
)
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Doesn't really answer to the topic, but piexil, you can use [img] tags to include the image in your post without users having to click on it ;)
For example, [img]http://i.imgur.com/0Nw1JxP.png[/img] gives that:
(http://i.imgur.com/0Nw1JxP.png)
)
Sweet, thanks! I haven't posted on forums in forever, so I forgot all of that.
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Change your window, and it should change too. I remember graphing sin(x)/x and finding that the graph would look like a sine function, and then changing the window size and it would be correct, even when only by less than a percent of the window size would recalculate it. I assumed that the calculator just graphed a number of points and found the best fit curve, and that is why these appear differently, but I don’t know for sure.
but I think it makes a taylor expansion to fit the function.
I thought almost all ti calculators use the CORDIC algorithm