How can you think of using the definition of infinity and infinitesimal when you see the question I asked

How can you think of using the definition of infinity and infinitesimal when you see the question I asked

The limit problem can be solved by equivalent substitution
For example, when X - > 0, X is equivalent to SiNx, arcsinx, TaNx, arctanx, (a ^ x-1) / LNA, [(1 + x) ^ B-1] / B, e ^ X-1, ln (1 + x)
You can use Lagrange's theorem, you can use Taylor's expansion, you can use lobida's law

Limit is infinity and limit does not exist. The book says "the limit of function is infinity". So for the limit of exponential function, can we say that the limit is infinity?
According to the necessary and sufficient condition of the existence of limit, when the right limit is equal, the limit of exponential function does not exist

In fact, "limit is infinite" is just a kind of limit nonexistence, which means that no positive number can be found, which is always greater than the value (or absolute value) of the function. And "limit nonexistence" means that when the independent variable of the function tends to a certain value, the value of the function is uncertain, such as the sum SN of the sequence 1-1 + 1-1 + 1... When n →∞, sometimes it is 0, sometimes it is 1, Its limit does not exist. Of course, infinity does not exist!

The one-sided limit of a and B points of continuous function on (a, b) is infinity (non positive infinity and negative infinity),

F (x) = TaNx, which is continuous on (- π / 2, π / 2), and the left limit at x = π / 2 is positive infinity, and the right limit at x = - π / 2 is negative infinity