Math enthusiast

Mathematics is not only the tool of knowledge, but also the source of other knowledge tools. All the science of research sequence and measurement is related to mathematics.

On the definition of function limit when the independent variable tends to infinity It is defined as "when X - > ∞, the function value f (x) is infinitely close to a certain constant a, then a is called the limit of function f (x) when X - > ∞"   Here, infinite approach means that in the process of X - > ∞, after (at least) a certain point x on the number axis, will the function value be closer and closer to a It means that at least after an absolute value, the greater the absolute value of X, the closer the function value is to a   So why does the following formula hold?   I can understand from the front to the back, but from the back to the front, I don't think it's necessary. The latter two formulas can only ensure the tendency of function values in one direction   For example, suppose the limit value is 6, When x = 3, it is assumed that the function value is   five When x = - 4, it is assumed that the function value is 4   And when | x | - >   When ∞ (from 3 - > - 4, absolute value from 3 - > 4), the function value is not closer to the limit value 6 What is the definition of function limit when the independent variable tends to infinity Can you think of it this way: Let me take some individual points as examples, When x = 1,2,3,4, the function value is 3,4,5,6   (close to limit 10) When x = - 1, - 2, - 3, - 4, the function value is 2, 4,6,8 (or 2,3,4,6) is also close to the limit value 10 Although not strictly according to the absolute value of | x | the greater the absolute value, the closer it is to the limit value 10 In this way, the function f (x) can still be counted as - > a  ?  lim f(x) = A   -------------------- Is it possible to "zigzag forward" towards the limit value of 10