Y = x + A / X constant a > 0 prove monotonicity of function

Y = x + A / X constant a > 0 prove monotonicity of function

Definition method: constant a > 0. When x > 0, it is divided into x ＞ A and 0 ＜ x ＜ A. when x ＞ a, y = x + A / X constant a > 0 is an increasing function. Similarly, it can be proved that when 0 ＜ x ＜ a, y = x + A / X constant a > 0 is a decreasing function. Because y = x + A / X constant a > 0 is an odd function and has the same monotonicity in the symmetric interval, when x ＜ - √ a, y = x + A / X constant a > 0 is an increasing function, When - a ＜ x ＜ 0, y = x + A / X constant a > 0 is a decreasing function;

The monotonicity of function y = 1 / (x ^ 2-1) is judged and proved

Prove: let y = 1 / u (x) U (x) = x ^ 2-1, x ^ 2-1 ≠ 0, X ≠ 1 or - 1
Y = 1 / u (x) is a decreasing function, u (x) is a decreasing function at (- infinity, - 1) and (- 1,0], and is an increasing function at [0,1) and (1, + infinity)
So y = 1 / (x ^ 2-1) is an increasing function in (- infinity, - 1) and (- 1,0); in [0,1) and (1, + infinity), it is a decreasing function

When solving the equations {5 / X-12 / y = 6,2 / x + 3 / y = 18, if 1 / x = m, 1 / y = n, then the original equation
When solving the equations {5 / X-12 / y = 6,2 / x + 3 / y = 18, if 1 / x = m, 1 / y = n, then the original equations can be transformed into {5m-12n = 6,2m + 3N = 18, and the solution is {M = 6, n = 2. So {1 / x = 6,1 / y = 2. So C = 1 / 6, y = 1 / 2. This method of solving the equations is called substitution method. Using the above method to solve the equations: {15 / x + y + 2 / X-Y = 5,10 / x + y-4 / X-Y = - 2

Let m = 1 / (x + y), n = 1 / (X-Y)
Then the equations become {15m + 2n = 5,10m + 4N = - 2}
The solution is {M = 3 / 5, n = - 2}
So 1 / (x + y) = 3 / 5, 1 / (X-Y) = - 2}
The deformation is {x + y = 5 / 3, X-Y = - 1 / 2}
The solution is {x = 7 / 12, y = 13 / 12}

If cos θ > cos30 & ordm, the value range of acute angle θ is?

COS is a decreasing function from 0 to 90 degrees earlier
So 0 degrees

For the algebraic expression ax ^ 5 + BX ^ 3 + CX + 8, when x = 3, its value is 70. When x = - 3, what is its value

x=3
Then a * 3 ^ 5 + b * 3 ^ 3 + 3C + 8 = 70
a*3^5+b*3^3+3c=62
x=-3
Original formula = a * (- 3) ^ 5 + b * (- 3) ^ 3 + C * (- 3) + 8
=-(a*3^5+b*3^3+3c)+8
=-62+8
=-54

Granny Zhang's family has 150 chickens and ducks. The number of chickens is five times that of ducks?

Duck: 150 (5 + 1) = 25; chicken: 25 × 5 = 125

What is Tan 2 degrees?

0.0349

1. The image of quadratic function y = ax2-5x + C intersects with X axis at a (1,0) B (4,0), and the analytic expression of quadratic function is obtained
2. It is known that the quadratic function y = ax2-2ax + B intersects the X axis at a (3,0) and the Y axis at C (0, - 9 / 4)

Solve problem 1: substitute x = 1, y = 0; X = 4, y = 0 into y = ax & sup2; - 5x + C to get the equation system:
0=a-5+c
0=16a-20+c
The solution is: a = 1, C = 4
So the analytic expression of quadratic function is y = x & sup2; - 5x + 4
Question 2: substituting x = 3, y = 0; X = 0, - 9 / 4 into y = ax & sup2; - 2aX + B to get the equations:
0=9a-6a+b
b=-9/4
The solution is: a = 3 / 4, B = - 9 / 4
So the analytic expression of quadratic function is y = (3 / 4) x & sup2; - (3 / 2) X-9 / 4

Given a (- 1, - 2) and B (1,3), the______ Translation______ The point B is symmetric about the Y axis

According to the law of symmetrical points in the plane rectangular coordinate system, the point B is symmetrical about the y-axis (- 1,3), and the point a (- 1, - 2), so the point (- 1,3) is obtained by translating the point a upward five unit lengths

Those with difficulty, such as parity, couplet, etc
Summary of concept and application of various functions
It's better to have examples

The first part of the collection (1) the number of subsets of the collection containing n elements is 2 ^ n, the number of true subsets is 2 ^ n-1; the number of non empty true subsets is 2 ^ n-2; (2) Note: don't forget the situation when discussing. (3) the second part of the function and derivative 1