I've been trying to study for my midterm and I don't understand how to solve this. My textbook doesn't seem to have anything written in it either. I know that this is a piece-wise function and I was able to solve for limits of basic polynomials, but this one is stumping me. Please help!
Evaluate lim f(x) and f(3), where
x ->3
f(x) = {1/ ((x-3)^2) if x does not equal 3
{ 2 if x=3
I am okay with solving when I can apply the left hand/right hand limit, but I have no idea what to do with this.
Evaluate lim f(x) and f(3), where
x ->3
f(x) = {1/ ((x-3)^2) if x does not equal 3
{ 2 if x=3
I am okay with solving when I can apply the left hand/right hand limit, but I have no idea what to do with this.
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f(3) = 2 because 3 belongs in the second piece
The limit as x→3⁺ or x→3⁻ is infinity, approaching a vertical asymptote at x=3. Then there's a point at (3,2) floating in the middle of the two branches of the graph. Therefore limit of f(x) as x→3 does not exist.
The limit as x→3⁺ or x→3⁻ is infinity, approaching a vertical asymptote at x=3. Then there's a point at (3,2) floating in the middle of the two branches of the graph. Therefore limit of f(x) as x→3 does not exist.
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They both go to +infinity, so if your teacher accepts "infinity" as an answer to a limit, then that's fine. But some calc teachers want you to say infinite limits do not exist.
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