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Zero point theorem and intermediate value theorem
Zero point theorem and intermediate value theorem
As long as it is a continuous function, the problem becomes clear. The continuity lies in the correspondence between an X and a y value
"Zero point" and "medium" both refer to a point on the function domain [X-axis], and the corresponding function value is 0 or a special value. This corresponding point on the x-axis is also called root in some cases
If f (x) = C, finding the intermediate value point is equivalent to finding the zero point for the function f (x) - C. that is, finding the point on the x-axis where the function = 0
In addition, the existence of "at least one" table is a problem;
"Unique" usually uses derivative method to determine the uniqueness by judging the trend of monotonicity
On this basis, when a derivative function is continuous, or an original function is second-order differentiable, then the mean value theorem can be understood as the intermediate value problem or the zero point problem of the derivative function
What is the existence theorem of zeros?
If f (x) is continuous on the interval [a, b], and f (a) f (b)
Problems of zero point theorem and intermediate value theorem
The premise of these two theorems is the closed interval gun continuous function, but why does he come to the conclusion that it is in the open interval? How about at least one point? Why do we have to emphasize the open interval and the closed interval?
The values of two endpoints have been determined, one is a, the other is B. therefore, it is impossible for these two endpoints to take a value C between a and B. for example, f (a) = 1, f (b) = 5, take a number between C = 1 and 5, for example, take 3, then the point equal to 3 may be a and B. therefore, the point equal to 3 can only be a point in the open interval (a, b)
Zero point theorem is a special case of intermediate value theorem
The function y = MX2 + x-2m (M is a constant), and the intersection of the image and X-axis has the following properties______ One
When m = 0, y = x, the intersection of image and X-axis has one
Product rule in Calculus
As shown in the picture
The first is the limit multiplication algorithm, and your expression is problematic. The first condition is that the limit of two functions exists. The second is the derivation (multiplication) algorithm. The derivation formula is derived from the limit, and the result is different. There is a derivation process in the book, you can have a look, and hope it can help you!
Two teachers of a school took several students to travel and contacted two tourism companies with the same price. After negotiation, the preferential condition of company a was that one teacher should pay the full price
Two teachers of a school took some students to travel and contacted two travel companies with the same price. After negotiation, company a offered a discount
The condition is that one teacher will be charged in full, and the rest will be charged at a discount of 7.5%. The preferential condition of company B is that all teachers and students will be charged at a discount of 8%
When the number of students exceeds, the other 7.5% discount; a travel company is more preferential than B travel company. 2) after accounting, the preferential price of a travel company is 1 / 32 cheaper than B company. How many students are there?
Linear equation of one variable
The process of finding the limit solution of LIM (x → 0) xcotx
&Thank you. I don't know
In the sequence an, if A1 = 1 and 1 / a (n + 1) is the second power of the base - 1 / A and N is the second power of the base = 4, then an=
1/a(n+1)^2-1/an^2=4
So {1 / an ^ 2} is equal difference
1/an^2=1/a1^2+4(n-1)=4n-3
an^2=1/(4n-3)
an=±√[1/(4n-3)],n∈N*
No, I don't know how to say it in English
Sorry,I don't know.
The square area is about 440000 square meters. How accurate is this approximation
Individual position
RELATED INFORMATIONS
- 1. The difference between the function differentiable in the closed interval and the function differentiable in the closed interval, why is the mean value theorem only required to be differentiable in the open interval? Why do mean value theorems only require derivability in open intervals? Closed interval is continuous, open interval is differentiable, so closed interval is differentiable? Explain why... I need a reason
- 2. The relationship between Lagrange's mean value theorem and Rolle's theorem
- 3. Rolle's theorem, Lagrange's mean value theorem and Cauchy's mean value theorem are generally applied to what questions?
- 4. Continuity of functions in higher numbers Discuss the continuity of the following functions and draw the f (x) graph 1. F (x) = LIM (n approaches infinity) 1 (1 + (cosx) ^ 2n) 2. F (x) = LIM (n approaches infinity) {[1-x ^ (2n)] \ [1 + x ^ (2n)]} * x Graphic words, a little description of what it looks like
- 5. The continuity of higher number function (concrete process) f(X)=1/xsinx,(x0) When we ask what the constant k is, f (x) is continuous in its domain?
- 6. How to prove that a function is unbounded on an interval Prove that y = 1 / X sin1 / X is unbounded on (0,1]
- 7. If the function f (x) is defined on [a, b] and | f (x) | is integrable on [a, b], does the integral of F (x) exist on [a, b]?
- 8. If the function f (x) defined on [a, b] is greater than 0, then its definite integral on [a, b] must be greater than 0? May it be equal to 0? Your answer is incorrect, because f (x) is not necessarily a continuous function. I already know how to prove it It's my first time to ask a question and see how quickly you reply to me,
- 9. The definite integral of periodic function on (a, a + T) has nothing to do with A. how to prove it? The definite integral of periodic function on (a, a + T) has nothing to do with A. how to prove it? F (x) = f (x + T). Find the definite integral of F (x) on [a, a + T]. The conclusion is that the definite integral is a definite value, that is, the definite integral of F on [0, t].
- 10. Calculation by using definite integral characteristic of periodic function ∫ (upper n π lower 0) | sinx| DX
- 11. Let a > 0, b > 0, prove that (x + a) 2 (X-B) + x2 = 0 has one positive root and two negative roots (zero point theorem and intermediate value theorem of higher numbers)
- 12. Some problems in "differential mean value theorem and derivative application" of higher numbers 1. Let f (x) be continuous on [0,1], derivable in (0,1), and f (0) = f (1) = 0, f (1 / 2) = 1 / 2. It is proved that for any C ∈ (0,1), there exists ξ∈ (0,1) such that f '(ξ) = C 2. It is known that f (x) is differentiable in R, and (x →∞) Lim f '(x) = E, (x→∞)lim [(x+c)/(x-c)]=(x→∞)lim [f(x)-f(x-1)] Finding the value of C
- 13. Ask questions about higher numbers 3 (about differential mean value theorem) Let B not be equal to a, and prove that | arctanb arctana | is less than or equal to | b-a|
- 14. It is proved that if the function f (x) satisfies the relation f '(x) = f (x) and f (0) = 1 in (- ∞, + ∞), then f (x) = e ^ X
- 15. Differential of composite function Known F[w*(1+t)]=K(w) Differential equation on both sides Why do you get it F'(dw + w*dt)=K' dw
- 16. There is a pile of yellow sand on the construction site. One quarter of the total amount was used in the first day, and one quarter more was used in the second day than in the first day. How many tons of yellow sand are left
- 17. 4 / 5 of a is equal to 2 / 3 of B, and a is a fraction of B
- 18. There are five consecutive even numbers, and their sum is 130. What are the five even numbers?
- 19. The distance between a and B is 40 km, the speed of motorcycle is 45 km / h, the speed of truck is 35 km / h, and the speed of truck is 35 km / h How long does it take for the same car to travel in opposite directions? The distance between the two cars is 10 kilometers?
- 20. It is known that a * 6 / 5 = 9 / 10 * b = 13 / 13 * C, and ABC is not equal to 0. Try to arrange ABC in the order of% d% a