The definition of bounded function If | f (x)|

The definition of bounded function If | f (x)|

If | f (x)|

Given X-Y = 2, xy = - 1, find the value of (4x-5y-xy) - (2x-3y + 5xy)

Process or answer

What is the upper bound and the lower bound of a function?

Let s be a set of numbers, and u be the set of all upper bounds of S. then there must be a minimum number in U. let the minimum number be beta, and beta is the supremum of S, and be beta = sup s
Let s be a set of numbers, and let l be the set composed of all the lower bounds of S, then there must be a maximum number in L. let alpha be the maximum number, and let alpha be the infimum of S, and let alpha be the infimum of S
(alpha, beta, just write letters. It's too inconvenient to type. Please forgive me...)
Mathematical analysis of definition from higher education press

If | x + 2 | + (Y-3) ∧ 2 = 0, find the value of XY ∧ 2 / 2x-3y
It is known that a = a + a Λ 2 + a Λ 3 + +A Λ 2004, if a = 1, then what is a equivalent to? If a is equal to - 1, then what is a equivalent to?

If | x + 2 | + (Y-3) ∧ 2 = 0, find the value of XY ∧ 2 / 2x-3y
It is easy to get x + 2 = 0, Y-3 = 0, x = - 2, y = 3,
The original formula = - 2 * 9 / - 4-9 = 18 / 13
It is known that a = a + a Λ 2 + a Λ 3 + +A Λ 2004, if a = 1, then what is a equivalent to? If a is equal to - 1, then what is a equivalent to?
When a = 1, a = 2004,
When a = - 1, a = 0

On the definition of function boundedness
Mathematically, if there is a positive number m in the range of variable x (expressed by D), the function value f (x) on D satisfies the following conditions
│f(x)│≤M ,
Then the function y = f (x) is said to be bounded on D
For a constant value function, can its absolute value be taken as the positive number m? If so, then for the function y = 0, can not m take zero? Why does m have to be a positive number

It's good that you can ask such a question
The example you gave is very special, that is, | f (x) | ≤ 0. Obviously, f (x) is equal to 0
Moreover, when m is satisfied with 0, then there must be a positive number M0
This means that the definition is OK
What's more, the definition says that there is a positive number m, but it doesn't say that 0 can't be taken as 0 in special cases
When we can take 0, we can certainly find a positive number to satisfy

If (2x + 1) 2 + | 3Y + 2 | = 0, then XY=

Because (2x + 1) 2 ≥ 0, | 3Y + 2 | ≥ 0, (2x + 1) 2 + | 3Y + 2 | = 0, so (2x + 1) 2 = 0, | 3Y + 2 | = 0, so 2x + 1 = 0, 3Y + 2 = 0, so x = - 0.5, y = - 2 / 3, so xy = 1 / 3

The definition of function boundedness
Definition: the domain of function f (x) is D, and the number set X is contained in D. if there is a positive number m, then
|f(x)|

The domain of a function may be very large, but we often only want to know whether it is bounded locally
For example, the definition field of F (x) = x ^ 2 is all real numbers, but if only the case of [0,10] needs to be considered due to the limitation of practical application, then the function is bounded, and f (x) = Tan x is unbounded even if the restriction is added
Using the expression that x is contained in D, we can choose the shape of the set we want. Because D is completely fixed by F, it is not conducive to discuss the local case

Is it right that the textbook is equal to - e ^ y?

∫e^(-y)dy=-∫e^(-y)d(-y)
=-e^(-y)
Is your answer wrong

What is the special solution of y = e when xdx + YDY = e ^ x satisfies x = 1
On the right is y|x = 1 = E
X = 1 in the lower right corner

The equation is wrong: the left is a total differential, but the right is a function. Do you lose DX or dy on the right?
----------------------------------------------------------------------
We have no doubt about what you added. You have not corrected the mistakes we pointed out