I was playing around with my calculator before finding out it has a graph feature, I inputted X^∞ and it came up with a straight line from -1 to 1, Im curious as to why it does this.
In: 2
What does 2^∞ means? It’s the answer to the question “If a population doubles every day, then how many peoples will there be at the end of time?” which is an infinite amount of peoples, so not something you can put on a drawing
What does (1/2)^∞ means? It’s the answer to the question “If a population halves every day, then how many peoples will there be at the end of time?” which is 0.
More generally:
*For x>1 then x^∞ =+∞, so not drawn.
*For x=1 then x^∞ =1, but your calculator might not be displaying it correctly.
*For -1<x<1 then x^∞ =0, which is the straight line you see.
*For x=-1 things are weird since x^∞ is equal to both -1 and +1 at the same times. Your calculator is probably considering that this is “undefined”, so not drawn.
*For x<-1 things are still weird and x^∞ is equal to both -∞ and +∞ at the same time. But in any case it’s not drawn.
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