What is the intermediate value theorem of continuous function

Let the function y = f (x) be continuous on the closed interval [a, b], then there must be the maximum and minimum function values in this interval: F (min) = a, f (max) = B, and a ≠ B. then, no matter what number C is between a and B, there is at least one point in the open interval (a, b) ξ, Make f（ ξ)= C (a< ξ

On the functional continuity of Higher Mathematics Y = xsin (1 / x) when x is not equal to 0 y = x squared xsin (1 / x) when x is not equal to 0 0 when x = 0 0 when x = 0 Explain why the differentiability of the two is different? The above is two piecewise functions. The topic is to discuss the continuity and differentiability at x = 0~

You'd better write the subject clearly
First function
According to derivative definition
The derivative of the function at x = 0 is
Lim [xsin (1 / x) - 0] / x = limsin (1 / x) (x tends to 0)
When x tends to 0, sin (1 / x) is an uncertain value, so this function is not differentiable at x = 0
Second function
According to derivative definition
The derivative of the function at x = 0 is
Lim [x ^ 2Sin (1 / x) - 0] / x = limxsin (1 / x) (x tends to 0)
When x tends to 0, xsin (1 / x) = 0, so the function is differentiable at 0 and the derivative is 0

What is the difference between the zero point theorem and Rolle's theorem of continuous functions on closed intervals

Rolle's theorem assumes that the function f (x) is continuous on the closed interval [abfjnb] (where a is not equal to b), differentiable on the open interval (a, b), and f (a) = f (b), then there is at least one point ξ ∈ (a, b), so that F & 39; （ ξ）＝ 0zdh zero point theorem let the function f (x) be continuous on the closed interval [a, b], and f (a) and f (b) have different signs (i.e. f (a)) × F (b) & lt; 0), then there is at least one zero point of function f (x) in the open interval (a, b), that is, at least one point ξ （a＆lt； ξ＆ Lt; b) make f（ ξ）＝ 095 this... Completely different theorem ah, how can V tell the difference between Pt? If there are similarities, that is, they are all properties of closed interval continuous functions

The sign law of three function values: the positive function in the first quadrant has () Fill in what

Quadrant 1: sin cos Tan cot sec CSC
Quadrant 2: sin CSC
Quadrant 3: Tan cot
Quadrant 4: cos sec

As an ideological and political theory course, what is the learning purpose of the outline of Chinese modern history? Talk about your learning experience Key points: 1. When answering questions, the focus should not deviate from the topic requirements of "as an ideological and Political Theory Course" 2. The textbook contents of the outline of modern Chinese history should be interspersed, such as the editor's "opening remarks" and "concluding remarks" 3. Of course, as an examination question, you have to have your own experience. I hope you can give a better experience I really hope you can give a good answer. I'm very grateful Forgot to say, everyone should answer according to my requirements! Word count requirement: 500-600. You can also write multiple points I sincerely hope to get your help

Don't tell me you can't do this. What the teacher wants is for you to talk about your learning experience. I suggest you write it yourself. Don't copy it from the Internet. What's more, the so-called experience is what you learn. Isn't the general situation of that book what you learn? Of course, the purpose is what you know. God, this is also copied from the Internet

When x tends to 0, limf (x) / x = 1, and f '' (x) > 0, it is proved that f (x) > = X

From limf (x) / x = 1, we know that f (0) = 0 and f '(0) = 1
Let g (x) = f (x) - X
G (0) = 0
g ' (x) = f ' (x) - 1
g' (0) = 0
g'' (x) = f ''(x)>0
So g (x) > = 0, the certificate is completed

What is the intermediate value theorem of continuous function