Find the lim of F(X) as X approaches zero
F(X) = 0/X ( Zero over X )
Well its a constant function equal to 0 for all values of x not equal to zero. So we can see the limit is equal to 0.
You could also use l'Hopital and get the same answer as Gib_Z provided.
Yeah it is zero but I want the lim without L'Hopital rule, I want the solution using Algebra.
Find the Lim of 0/X as X approaches zero.
0/X = X-X/X = X/X - X/X = 1-1 = 0
alternatively you can say that if y is a member of the the Reals then 0*y=0 set y=1/x. While not wrong, your solution simply overcomplicates things.
no matter what x is, the answer will always be 0. unless x = 0, then it is undefined. so you can say it is just approaching 0
f(x) approaches L as x goes to a if and only if f(x_n) approaches L for any sequence of numbers x_n approaching a.
Let x_n be any sequence of numbers approaching 0. What is 0/x_n? What is the limit of that sequence.
I don't know anything about Sequence limits.
But you ask of the limit of continuous functions?
Do you know the definition of a limit? If so it is obviously zero.
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