![](data:image/svg+xml;utf8,<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" viewBox="0 0 72 71" width="72"></svg>)
Definition of bounded function and unbounded function? Are some functions with lower bounds, such as quadratic function of y = x ^ 2, unbounded functions
I don't know the definition of bounded function and unbounded function, but the following understanding is certainly correct
In the domain of definition, the value of function has upper and lower bounds
Y = x ^ 2 if the value of the independent variable is not specified, then y is unbounded, because there is no upper limit, but if the value of X is specified as (- A, a), then the function is bounded
How to prove that a function is differentiable in a certain interval?
The piecewise function is derived according to the derivative formula in each segment and the definition at the piecewise point
If a function is unbounded in the interval, is its derivative and original function unbounded in the interval
Error! The simplest example is y = x unbounded, its derivative function is y = 1. And. Y = 1 is a single valued constant function, bounded in the interval
On the interval [1 / 2,2], the function f (x) = x & sup2 + BX + C (B, C ∈ R)
If G (x) = (X & sup2 + X + 1) / X has the same minimum value at the same point, then the maximum value of F (x) in the interval [1 / 2.2] is?
When x > 0
g(x)=(x²+x+1)/x=x+1/x+1≥3
If and only if x = 1 / x, that is to say, when x = 1, G (x) has a minimum value of 3
F (x) and G (x) have the same minimum value at the same point, that is, the vertex coordinates of F (x) are (1,3)
So f (x) = (x-1) ^ 2 + 3,
So the maximum value of F (x) = f (2) = (2-1) ^ 2 + 3 = 4
How to calculate 67 + 73 + 55 + 29 + 42 + 69 simply
= 67+37+55+30-1+40+2+70-1
=140+55+30+40+70
=280+55
=335
Let f (x) = a-22x + 1 (1) prove that f (x) is an increasing function; (2) find the value of a so that f (x) is an odd function; (3) find the range of F (x) when f (x) is an odd function
(1) It is proved that: let x1, X2 ∈ R, and x1 ＜ X2F (x1) - f (x2) = a-22x1 + 1-A + 22x2 + 1 = 2 (2x1 − 2x2) (2x1 + 1) (2x2 + 1) (2 points) ∵ y = 2x increase on (- ∞, + ∞), while x1 ＜ x2 2x1 ＜ 2x2 2x1-2x2 ＜ 0 (4 points) and (2x1 + 1) (2x2 + 1) ＞ 0 ∵ f (x1) - f (x2) ＜ 0, that is, f (x1) ＜ f (x2) ∵ f (x) is an increasing function on (- ∞, + ∞)（ 2) F (x) is an odd function, f (0) = A-220 + 1 = A-1 = 0 a = 1. It is tested that f (x) is an odd function (10 points) when a = 1. (3) from (2), f (x) = 1-22x + 1 ∵ 2X + 1 ＞ 1 ∵ 0 < 12x + 1 < 1 ∵ f (x) ∈ (- 1, 1) (14 points)
Square side length increases 5 centimeters, area increases 75 centimeters, seek original square side length and area
Let the side length of the original square be x, then (x + 5) (x + 5) = x.x + 75, the solution is x = 5, so the side length of the original square is 5cm and the area is 25cm
How to calculate 24 points with 3, 11, 2 and 8
2 times 8 plus 11 minus 3
Let the sum of the first n terms of the sequence an be Sn, and an ≠ 0, S1, S2, S3 If it is an equal ratio sequence, then the sequence A1, A2, A3 Is it an equal ratio sequence
Not an equal ratio sequence
Suppose {an} is an equal ratio sequence
When q = 1, Sn = Na1 is an arithmetic sequence
When Q ≠ 1, Sn = A1 (1-Q ^ n) / (1-Q)
{1-Q ^ n} is not an equal ratio sequence
So {Sn} is not an equal ratio sequence
A square needs 5400 pieces of cement square bricks with a side length of 4 decimeters. How many pieces of cement square bricks with a side length of 6 decimeters
X blocks are required
4*4：6*6=X：5400
36X=5400×16
36X=86400
X=86400÷36
X=2400
It costs 2400 yuan
Why 4 * 4:6 * 6 = x: 5400
16 should correspond to 5400. Why does it correspond to ×
The larger the area of the floor tile, the less the number of tiles needed
The number of tiles required is inversely proportional to the area of each tile
∴ 4×4∶6×6＝x∶5400
RELATED INFORMATIONS
- 1. Is unbounded function multiplied by bounded function or unbounded function?
- 2. The function f (x) = 1 / xsin1 / X is unbounded Why let x = 1 / (2n π + π / 2)? I mean, how can we find such numbers? Why not something else/
- 3. Ask a problem of periodic function on higher numbers There is a paragraph in the tutorial as follows: If f (x) is a function with period T, then the period of F (AX) is t / A, where a > 0 It is proved that f (x) is periodic with T, so for any x, f (x) is periodic F (AX + T) = f (AX), then f [a (x + T / a)] = f (AX), that is to say, f (AX) has a period of T / A I can't figure out how f (AX + T) = f (AX) came from. Please tell me,
- 4. Is y = xcosx bounded in (- ∞, + ∞) and infinite when x →∞ Let x (k) = 2K π, (k = 1,2,3,...) why can we do this... Is the definition field of X not a real number
- 5. The image of the function y = - xcosx,
- 6. The graph of the function y = xcosx + SiNx is approximately () A. B. C. D.
- 7. It is proved that the function y = x2 + 1 is a decreasing function in the interval (0, + ∞), Y = - x2 + 1 is a decreasing function in the interval (0, + ∞). Sorry, wrong number
- 8. Why monotone bounded function may not have limit and monotone bounded sequence must have limit. This paper analyzes the essential difference between the limit of function and sequence
- 9. Higher numbers for postgraduate entrance examination - using monotone bounded criterion to prove the existence of sequence limit Let a > 0, X1 = root sign (2 + a), xn + 1 = root sign (2 + XM) prove the existence of LIM n - > infinite xn and find its value
- 10. Given: x-xy = 40, xy-y = - 20, finding: x + y =? Is a problem in grade one of junior high school,
- 11. What are the definitions of bounded and unbounded functions and how to judge whether a function is bounded or unbounded? Let me start with a few questions 1. Is f (x) ∈ (a, b), f (x) bounded? G (x) ∈ [a, b], the upper bound of G (x) is B, the lower bound is a, which should be right 2. Functions with limits are not necessarily bounded? For example 3. Does f (x) unbounded represent f (x) →∞ when x ∈ (a, b), or other?
- 12. A function problem in Higher Mathematics If a company produces a product and can sell it all, the revenue function is r = 36x-x quadratic / 20, where x is the daily production of the company. If the daily production of the company increases from 250 to 260, please estimate the increase of the company's revenue It's necessary to explain the text and the steps, We should use the function method of higher mathematics, not the method of elementary school, complete steps, instructions and results
- 13. How to prove that the function f (x) = 2sinx-x + 1 is continuous on the closed interval [0,3]? Such as the title
- 14. How to solve the problem of definite integral of even function? Remember there is an example that we should pay attention to the symmetric interval for definite integral. If we directly solve it, we will get the wrong result. We need to use the law of even times odd zero to solve it. Can we give such an example?
- 15. Definite integral of piecewise function f(X)={ sinX (0
- 16. If the integrand is continuous, must its definite integral be continuous?
- 17. The definite integral of the product of integrable functions is equal to the product of their respective definite integrals A right B wrong
- 18. The definite integral exists. There are finite discontinuities on AB and they are bounded. Are discontinuities all kinds of discontinuities
- 19. Calculation by using definite integral characteristic of periodic function ∫ (upper n π lower 0) | sinx| DX
- 20. 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].