Question

Let f be a function defined on A

{a}, where a is a limit point of A.
lim ₓ → a f(x)=[infinity] if ∀ M>0, ∃δ>0

Answer 1

The given question is asking about a function and its limit at a specific point. The limit of the function f(x) as x approaches the limit point a is infinity, meaning that the function can increase without bound. The condition ∀ M>0, ∃δ>0 indicates that no matter how large a positive number M is chosen, there will always be a range of x values around the limit point a where the function is greater than M.

Step-by-step explanation:

The given question is asking about a function and its limit at a specific point. The notation used in the question, lim ₓ → a f(x)=[infinity], suggests that the limit of the function f(x) as x approaches the limit point a is infinity.

This means that as x gets arbitrarily close to a, the value of f(x) becomes arbitrarily large (infinite). The condition ∀ M>0, ∃δ>0 indicates that for any positive number M (no matter how large), it is possible to find a positive number δ such that the function f(x) is greater than M for all x within a certain range around the limit point a.

In simpler terms, this means that the function f(x) can increase without bound as x approaches the limit point a.