What is the limit of this function?

I don't have df. in my notes, but is that correct?
So without looking at the solution I proceeded like this:
lim(2x-x^2)/2x
x->o

So I have factored out an x ​​in the numerator: x(2-x)/2x
I then shortened the x, so I get
2-x/2
2-0 is 2
2/2 are then 1

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Rhenane
10 months ago

“Mathematic” would of course be otherwise noted (always with the “lim” in advance), but the procedure and the result would be correct.

You have a function with (re)removable definition gap at x=0. By shortening the x out, you get a straight line (temmed in normal form: f(x)=-1/2x+1), only that in this case the point (0|1) does not exist because the “un shortened” function for x=0 is not defined.