Given that the zeros of quadratic function f (x) = square of X + MX + n are - 1 and 2, then the solution set of inequality f (x) > 0 is

Given that the zeros of quadratic function f (x) = square of X + MX + n are - 1 and 2, then the solution set of inequality f (x) > 0 is

Because there are two zeros, Let f (x) = (x + 1) (X-2)
So x > 2 or X

How to prove the existence of limit of monotone bounded function

Higher mathematics (Volume 1 of the sixth edition, mathematics of Tongji University) page 53 has the process of proof

If a function limit exists, then it is locally bounded. Is there any relationship between the limit a and m in the boundedness?

If the function f (x) exists in the limit of x = x0, then there exists a small neighborhood f (x) bounded of x = x0, or if x tends to infinity, then there exists a sufficiently large positive number X. if | x | > x, f (x) is bounded. And if m and a have such a relationship, we suggest that you study mathematical analysis

Are all functions with limits bounded?

For example, when y = 1 / x, X tends to infinity, the limit is 0. It is not a bounded function

The continuous function has limit, and the necessary and sufficient condition of differentiability is that the function is continuous and the left and right limits exist and are equal

The existence and equality of left and right limits of continuous functions means that the left and right limits of LIM (f (x)) at x0 exist and are equal
The existence and equality of left and right limits of derivatives means that the left and right limits of LIM {(f (x) - f (x0) / (x-x0)} at x0 exist and are equal

A necessary and sufficient condition for a function to have a limit
I have been wondering whether piecewise functions can be said to have limits?
Suppose it has a breakpoint. I know that every segment of it has a limit, and the region is every segment. But when I define its region as (left infinity, right infinity), does it have a limit?
I don't know how to play the last eight, just make do with it!
Hope to have a reply as soon as possible
Similar to 1 x > 0
f(x) 0 x=0
—1 x

Function as a whole can not be said to have no limit, only discuss whether it has limit at a certain point
Piecewise function discusses the limit of the breakpoint to see if the left and right sides are equal. If they are equal, they will exist. If they are not equal, they will not exist
At infinity, the limit of positive infinity and negative infinity should be solved separately, because x can not tend to positive infinity and negative infinity at the same time

If the limit of one function exists, so does the limit of the other?
lim[f(x)+g(x)]=A
limf(x)=a
So limg (x) = A-A?

Yes, you can set F + G = H
Because of the existence of the limit of H and F, it is deduced from the related theorem
And limg (x) = limh (x) - limf (x) = A-A

Judgment questions
7. The limit of multivariate function is a function of one variable
Right and wrong

cuowu

What is the relationship between the existence of limit, the continuity and differentiability of function?

Derivable must be continuous
Continuity is not necessarily differentiable
The existence of limit is not necessarily differentiable
There must be a limit for derivability

What is the concept of limit existence of function?
.

The existence of limit means:
When x takes a certain value, when substituting x into a function or expression, it may be able to calculate a certain value, or it may not be substituted at all, because when substituting, there are unreasonable situations such as zero denominator
However, when x tends to this value, the value calculated each time tends to a fixed value, or closer and infinitely closer to this fixed value. We say that the limit of this function exists at this point