The monotonicity of function y = 1 / X is judged and proved emergency

The monotonicity of function y = 1 / X is judged and proved emergency

Because x ≠ 0, it can be divided into two interval analysis (- ∞, 0) and (0, + ∞)
There is X1 in the same section

It is proved that the function y = x - 1 / X is monotonically increasing on (0, + ∞). It is proved that the function y = x - 1 / X is monotonically increasing on (0, + ∞)
Beginners understand

Let x1, X2 in (0, + ∞) be any one, let X1 > 0, so x1 × x2 > 0
So f (x2) - (x1) > 0
So the function y = x - 1 / x increases monotonically on (0, + ∞)

It is proved that the function y = x + 1 / X is monotonically increasing on (0, + ∞). It is proved that the function y = x + 1 / X is monotonically increasing on (1, + ∞)

Y = x + 1 / X decreases on (0,1) and increases on (1, + ∞)
Let x2 > X1 > 0, then
f(x2)-f(x1)=(x2-x1)-(x2-x1)/*(x2*x1)=(x2-x1)*[1-1/(x2*x1)]
If 0, then f (x2) - f (x1) > 0 is an increasing function at (0,1)

What is the equation of a line with an intercept of - 3 on the Y axis and perpendicular to the line 2x + 3y-1 = 0?

From 2x + 3y-1 = 0, we can get y = - 2 / 3 * x + 1 / 3, so its slope is - 2 / 3,
The obtained line is perpendicular to it, so the slope of the obtained line is k = 3 / 2,
Therefore, the equation can be obtained as y = 3 / 2 * x-3 (or reduced to 3x-2y-6 = 0)

A simple method of 53 × 60 + 530 × 24?
Two ways?

53×60+530×24
=530×6+530×24
=530×(6+24)
=530×30
=15900

It is known that the line y = KX + B intersects with the X axis at the point (1,0), and intersects with the line y = 2x-3 and Y axis at the same point
Anxious! Anxious! Please reply immediately! Before 8:45!

The analytic expression of y-axis is x = 0 and y = 2x-3, and the intersection point is (0, - 3)
Substituting point (0, - 3) and point (1,0) into line y = KX + B
The solution is y = 3x-3

If a, B and C are in equal proportion sequence, then the number of common points of the image and x-axis of the function y = AX2 + BX + C is 0

Then AC = B & # 178;
The discriminant B & # 178; - 4ac = B & # 178; - 4B & # 178; = - 3B & # 178;
There is no zero in the proportional sequence
So B ≠ 0
So the discriminant - 3B & # 178;

It takes 2.57s for the radio wave to reach the moon and return to the earth. The known radio wave travels 3 × 105km per second, and the distance between the earth and the moon is calculated

12 × 2.57 × 3 × 105 = 3.855 × 105 ≈ 3.86 × 105 (km). A: the distance between the earth and the moon is about 3.86 × 105 km

For the inequality ax ^ 2 + BX + C > 0, the solution set is interval (- 1 / 2,2). For the coefficients a, B, C,
The results are as follows: 1) a > 0.2) b > 0.3) C > 0.4) a + B + C > 0.5) A-B + C > 0
The answer is 234
Why?

The reason is as follows: because of the inequality a (x ^ 2) + BX + C & gt; 0, the solution set is interval (- 1 / 2,2), which shows that the image of quadratic function y = a (x ^ 2) + BX + C is: the opening is downward, and the coordinates of the two intersections with X axis are (- 1 / 2,0), (2,0) respectively

If the point representing the number a on the number axis is to the left of the origin, the result of simplifying | 2A + A2 | is ()
A. -aB. -3aC. aD. 3a

On the number axis, the point representing the number a is on the left side of the origin, a < 0, A2 = | a | = - A, A2 + A2 | = | 2a-a | = | a | = - A