Can all rational numbers be represented by points on the number axis

Can all rational numbers be represented by points on the number axis

Yes, yes. The point on the number axis can represent any rational number
Yes, a number can be represented on the number axis
yes
yes
The points on the number axis and______ One to one correspondence
The point on the number axis corresponds to the real number one by one
The limit of multivariate function: the limit of XY ratio (2-e ^ XY minus 1 under the root sign)
Let u = XY → 0
Original formula = Lim U / [√ (2-e ^ u) - 1]
= lim 1/[-e^u / 2√(2-e^u) ]
= -2
Given the function f (x) = x2 + 2xsin θ - 1, X ∈ [- √ 3 / 2,1 / 2] when θ = Π / 6, find the maximum and minimum of F (x)
When θ = Π / 6,
f(x)=x2+2xsinθ-1=f(x)=x2+x-1=（x+1/2)＾2-5/4
Because x ∈ [- √ 3 / 2,1 / 2]
Obviously, for quadratic functions
When x = - 1 / 2, the minimum value of the function is - 5 / 4
And because 1 / 2 + 1 / 2 = 1 > - 1 / 2 + √ 3 / 2, so
When x = 1 / 2, the maximum value of the function is - 1 / 4
How to prove that the limit of binary function XY / x + y does not exist! Both of them tend to 0. Why do I think we can multiply 1 up and down/
How to prove that the limit of binary function XY / x + y does not exist! Both of them tend to 0. Why do I think we can multiply 1 / XY up and down to get the limit of 1 / 2? I don't remember the previous ones
Let x + y = KX ^ 2, then y = KX ^ 2-x
If y is introduced, XY / (x + y) = (kx-1) / K can be obtained
Because x approaches 0, XY / (x + y) = - 1 / K
Therefore, the limit value does not exist
(in my opinion, there is no theoretical basis for your practice. It seems that 1 / x + 1 / y is not greater than or equal to 2.)
Let x + y = KX ^ 2, then y = KX ^ 2-x
If y is introduced, XY / (x + y) = (kx-1) / K can be obtained
Because x approaches 0, XY / (x + y) = - 1 / K
Therefore, the limit value does not exist.
In my opinion, there is no theoretical basis for your practice. 1 / x + 1 / y is not greater than or equal to 2-_ -||Because I don't think 1 / x 1 / y tends to 1 when x y tends to 0. I'd like to ask the general idea of doing this kind of problem
Let x + y = KX ^ 2, then y = KX ^ 2-x
If y is introduced, XY / (x + y) = (kx-1) / K can be obtained
Because x approaches 0, XY / (x + y) = - 1 / K
Therefore, the limit value does not exist.
In my opinion, there is no theoretical basis for your practice. 1 / x + 1 / y is not equal to or greater than 2-_ -||Because I think when x y tends to 0, 1 / x 1 / y doesn't tend to 1? I want to ask what's the general idea of doing this kind of problem and what's the relationship between K. I didn't listen to it in class. Now I don't know what to do-_ -||Thank you
Given the function f (x) = (a + SiNx) / (2 + cosx) - BX (1), if f (x) has a maximum and a minimum on R, and its maximum is
For detailed solution, it comes from [2010 Suzhou three mode] (1) f (x) = (a+sinx/2+cosx) -bx, (1) if f (x) has the maximum and minimum value on R, and the two and 2680, seek a, B.
(2) If f (x) is odd
1, whether there is a real number B, where f (x) is an increasing function at (0,2 / 3 π) and (2 / 3 π, π) is a decreasing function
B = 0, a = 1340 (1) f (x) = 1 + A-2 (SiNx / 2) ^ 2 + SiNx / 2-bx. Y = 1 + A-2 (SiNx / 2) ^ 2 + SiNx / 2 is a bounded function. Y = - BX is divergent when B is not equal to 0. B = 0, M = MAXF (x), n = minf (x). This is a problem of quadratic function of one variable. When SiNx / 2 = 1 / 4, M = 9 /
b=0,a=2010
Y = (a + SiNx) / (2 + cosx) is a bounded function, and y = - BX is divergent when B is not equal to 0, no matter b > 0 or b 0 or b 0
Let f (x, y) = XY ^ 2 / (x ^ 2 + y ^ 4); (x, y) not equal to (0,0) 0; (x, y) = (0,0) judge the limit and continuity of F (x, y) at point (0,0)
This function is divided into (x, y) equal to 0 and not equal to 0. One gets the function formula, and the other gets 0. I only know that let x = KY ^ 2, and then substitute it into the first function formula, and the result of simplification is K / (k ^ 2 + 1). Then how to judge it will not happen, as if the result of simplification must be constant. By the way, if you can explain the detailed relationship between limit and continuity, Generally how to judge, let me have a good grasp, that's better
F (x, y) = XY ^ 2 / (x ^ 2 + y ^ 4); (x, y) is not equal to (0,0)
0 ; (x,y)=(0,0)
If a function of many variables wants to have a limit, it must and only if (x, y) tends to (0,0) in any way,
The function f (x, y) has the same way. In general, we don't use this conclusion when proving the existence of function limit, because it is more troublesome
But when we prove that limit does not exist, we use the opposite of this conclusion: limit does not exist if and only if there are two different ways, so that
The limit of function is not equal
You find two different ways: x = KY ^ 2, and as K changes, there are countless ways to go to the origin,
In these ways, the limit is K / (k ^ 2 + 1), which also changes with different ways, so the function limit does not exist
In addition, if the function is continuous at this point, then the function limit must exist and be equal to the function value of the change point. This is a necessary and sufficient condition
On the contrary, the limit does not exist, or the limit exists but is not equal to the value of the function
These are the most basic definitions that need to be remembered
The sum of the maximum and minimum values of the x power of the function y = a on [0,2] is 3. What is the maximum value of the function y = 3ax-1 on [0,1]?
This is a problem in mathematics compulsory one of senior one
For senior one students: a > = 0
The exponential curve y = a ^ x is a monotone function, and the maximum and minimum values are at the two ends of the interval [0,2], that is
a+a^2=3
The positive solution of a = ((13) ^ (1 / 2) - 1) / 2 is obtained by solving the equation
The function y = 3 * a * X-1 is monotone,
Find y (0) = - 1
y(1) = (3/2)*( 13^(1/2) -1 ) - 1
y(1)>y(0)
Y (1) is the maximum
HDU 1018 (find the number of digits of a factorial)
(1) To find out the meaning of the question is to find the number of digits of a factorial
(2) Use the mathematical formula (Stirling formula: lnn! = nlnn-n + 0.5 * ln (2 * n * PI)) to calculate the number of digits
Note: the format of the output
Feeling: but at the beginning of the problem, how to find a number factorial
It's really impossible to start with the number of digits. Only by searching the method on the Internet can we start with it
Section, he is still very weak, need to strengthen
code:
#include
#include
#define pi 3.14159265
int num,result;
void JC()
{
double t;
t = (num*log(num) - num + 0.5*log(2*num*pi))/log(10);
result = (int)t+1;
printf("%d\n",result);
}
int main()
{
int i,n;
scanf("%d",&n);
for( i=0 ; i
The number of n-th power factorial is equal to log10 (n!) rounded and 1
It is known that the maximum value of y = a-bcos (2x + π / 6) (b > 0) is 3 / 2 and the minimum value is - 1 / 2
1. Find the value of a and B
2. Find the minimum value of function g (x) = - 4asin (BX - π / 3) and the set of corresponding X
(1)
Because b > 0
When cos (2x + π / 6) = - 1, there is a maximum
a+b=3/2 1
When cos (2x + π / 6) = 1, there is a minimum
a-b=-1/2 2
1 + 2
a=1/2
Formula 1-2
B=1
(2)
g(x)=-4*(1/2)sin(1x-π/3)
=-2sin(x-π/3)
When sin (x - π / 3) = 1, there is a minimum value of - 2
That is X - π / 3 = 2K π + π / 2
x=2kπ+5π/6
a＋b=3/2
a－b=-1/2
a=1/2,b=1
g(x)=-2sin(x-pai/3)
Minimum - 2
Take the minimum x-pai / 3 = Pai / 2 + 2kpai
x=5pai/6+2kpai
K is an integer