![](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>)
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?
As long as it's about odd and even functions
1. First of all, look at the domain, see if the domain is symmetric about the origin, such as (- 1,1) symmetry
If y = cos, X is even function in the range of real number, then it is non odd and non even function in [- 3,4]
2. If f (- x) = f (x), then it is an even function, and f (- x) = - f (x) then it is an odd function. If you choose or fill in the blank, you can substitute two numbers to see. For example, - 1 and 1. Are odd functions and defined at 0, then f (0) is equal to 0
If f (x) = 1 / x, it is not an odd function on X ∈ R
How to prove that 2 ^ x + (1 / 2) ^ x is an increasing function in the range of positive real number
f(x)=2^x+(1/2)^x
f'(x)=ln2*2^x+ln(1/2)*(1/2)^x
=ln2*(2^x-1/2^x)
x> 0. 2 ^ x > 1 > (1 / 2) ^ x, LN2 > 0
F '(x) > 0
Given that the function f (x) = the cube of X + X, for any real number m belonging to [- 2,2], there is f (mx-2) + F (x)
f(x)=x³+x,
F (- x) = - X & sup3; - x = - f (x), so the function is odd
The functions y = x & sup3; and y = x are increasing functions on R,
So f (x) = x & sup 3; + X is also an increasing function on R
f（mx—2）+f（x）
The sum of each digit of a three digit number is 17. The ten digit number is larger than the one digit number. 1. If the hundred digit number of the three digit number is swapped with the one digit number to get a new three digit number, the new three digit number is 198 larger than the original three digit number
Let the original number be a, then the tens are a + 1, and the hundreds are 16-2a. According to the equation 100A + 10 (a + 1) + 16-2a-100 (16-2a) - (10a + 1) - a = 198, the solution is a = 6, then a + 1 = 7, 16-2a = 4. A: the original number is 476
Mathematics problems (grade one of junior high school), the problems that must be done today, the speed and quality are better
1. When m takes what value, the value of the algebraic formula 4m-5 / 3 is 5?
2. Given that the solution of the equation AX + 2 = 4-x about X is 1 / 2, find the value of A
3. Now the age of a son is 3 / 10 of that of his father. Eight years ago, the age of a son was only 1 / 8 of that of his father?
4. Three classes in grade one donated books to hope primary school. Class one donated 152 books. The number of books donated by class two is the average of the three classes. The number of books donated by class three is 40% of the grade. How many books did the three classes donate?
1. When m takes what value, the value of the algebraic formula 4m-5 / 3 is 5? 4m-5 / 3 = 5m = (5 + 5 / 3) / 4m = 5 / 32. It is known that the solution of the equation AX + 2 = 4-x is 1 / 2, and the value of a is obtained. 1 / 2x + 2 = 4-1 / 21 / 2x + 2 = 7 / 2x = 33
The equations of the two adjacent sides of the parallelogram are X-Y + 1 = 0 and 3x + Y-3 = 0 respectively, and the intersection of the diagonals is m (0, - 1)
The equations of the two adjacent sides of the parallelogram are X-Y + 1 = 0 and 3x + Y-3 = 0 respectively, and the intersection of the diagonals is m (0, - 1)
Note that the intersection of the line X-Y + 1 = 0 and 3x + Y-3 = 0 is the vertex a of the parallelogram ABCD. Solve the equations and get a (1 / 2,3 / 2). Because the intersection of the diagonal is m (0, - 1), the coordinates of the vertex C are (- 1 / 2, - 7 / 2). The equation of the line passing through C (- 1 / 2, - 7 / 2) and parallel to X-Y + 1 = 0 is x-y-3 = 0; the equation passing C (- 1 / 2, - 7 / 2) and parallel to X-Y + 1 = 0 is x-y-3 = 0; the equation passing C (- 1 / 2, - 7 / 2) and parallel to 3
A simple algorithm of 99 / 101 × 102
101×99/102
＝（102－1）*99/102
＝102*99/102－99/102
＝99－99/102
= 98 and 3 / 102
= 98 and 1 / 34
Fill in the blanks and multiple choice questions in Mathematics
1、 If x + y = 1, then 5-x-y=_____ . 2, () - (2x ^ 2 + 2x-1) = x ^ 2-3x. 3. The perimeter of the triangle is 48, the first side is 3A + 2B, the second side is 2 times less than the first side by a-2b + 2, then the third side of the triangle is () a.49-4a-4b b.50-8a-8b c.50-4a d.51-4a. The mobile phone can't get the format, please. It's urgent to do your homework
There is a trapezoid. If the upper bottom is increased by 4cm and the lower bottom and height remain unchanged, it becomes a parallelogram and its area is increased by 10 square centimeters
When the upper bottom is reduced by 3cm and the lower bottom and height remain unchanged, it becomes a triangle?
Because the top and bottom increased by 4cm, its area increased by 10 square centimeters
Therefore, the newly added triangle area is 10, and the height can be calculated as 5
Because the upper bottom is reduced by 3cm, the lower bottom and height remain the same, then it becomes a triangle
So the upper bottom = 3, the lower bottom = 3 + 4 = 7
Height = 5
So area = (3 + 7) * 5 / 2 = 25
How to simplify the calculation?
38.1÷1.25
=（38.1×8）÷（1.25×8）
=304.8÷10
=30.48
RELATED INFORMATIONS
- 1. How to prove that the function f (x) = 2sinx-x + 1 is continuous on the closed interval [0,3]? Such as the title
- 2. 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
- 3. 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?
- 4. Definition of bounded function and unbounded function? Are some functions with lower bounds, such as quadratic function of y = x ^ 2, unbounded functions
- 5. Is unbounded function multiplied by bounded function or unbounded function?
- 6. 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/
- 7. 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,
- 8. 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
- 9. The image of the function y = - xcosx,
- 10. The graph of the function y = xcosx + SiNx is approximately () A. B. C. D.
- 11. Definite integral of piecewise function f(X)={ sinX (0
- 12. If the integrand is continuous, must its definite integral be continuous?
- 13. The definite integral of the product of integrable functions is equal to the product of their respective definite integrals A right B wrong
- 14. The definite integral exists. There are finite discontinuities on AB and they are bounded. Are discontinuities all kinds of discontinuities
- 15. Calculation by using definite integral characteristic of periodic function ∫ (upper n π lower 0) | sinx| DX
- 16. 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].
- 17. 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,
- 18. 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]?
- 19. How to prove that a function is unbounded on an interval Prove that y = 1 / X sin1 / X is unbounded on (0,1]
- 20. 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?