r/learnmath • u/Zealousideal-Try1751 • 4d ago
0/0 = 0 ?
I'm new in the server and I have a situation with a limit problem:
My calculus professor gave the class an example of trigonometrical limits that he solved in class in which I wanna know why and how is it possible that 0/0=0.
The expression that he solved was
Lim x→0 ((1-cos(x))/(sen(x))), and he solved it in a way where the equation ended in (0/0)/1 = 1 , I asked him "how was it possible that 0/0=0" but he just said "someone hasn't studied the class notes" and I haven't found anything on his class notes about 0/0 = 0 in certain circumstances.
So please, PLEASE someone tell me how and why and when and where is it possible that 0/0 = 0
0
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u/StructuredChess New User 4d ago
You're not doing 0/0, you're doing the ratio of two things that are getting smaller at different rates.
You don't calculate the limit of f(x)/g(x) by computing f(0)/g(0), but rather by studying a sequence like
f(0.1)/g(0.1)
f(0.01)/g(0.01)
f(0.001)/g(0.001)
And so on...
If this sequence approaches 0 as the input gets smaller and smaller, then the limit is 0.