Limit is a very useful way to study the behavior of functions.
Limit can be used to determine whether the function is near a fixed point of x0 (one side is only one-dimensional left and right), or whether it tends to a certain value when ±∞.
The definition of the derivative is derived from the limit, so the derivative of the undefined point can only be calculated with the limit.
Anomalous integrals are generally used to first use the basic theorem of calculus to obtain the original function, and then calculate the limit of the anomalous point of the original function to obtain the definite integral value
It is very important to learn the limit well, because the old man is always willing to investigate the use of the limit wherever the definition can be mixed.
There are many ways to calculate the limit, and the commonly used ones are [Substitution of certain value], [Important limit], [Equivalent infinitesimal substitution], [Taylor expansion, McLaughlin's formula]... and actually the person who asked the question asked you not to use it "Lobida's Law"
The limit is very much needed [determined value], which is very difficult for me in the initial learning, because I don’t know how to change a value that I can’t get in elementary calculations, or if I understand it wrong and get a 0 result. Correct... In addition, the understanding of [high-order infinitesimal] is also very important, because this "gap" is the degree of acceptable error that we cannot understand in our elementary calculations.
The definition of the limit will not be considered much, but the derivative and anomalous integral defined by the limit often require the calculation of the limit.