The method of finding the range of fractional function For the form y = ax ^ 2 + BX + C / ex ^ 2 + FX + G and the function domain is not r (such as x > 0), the general method is to find the range ----------- Note that the general solution, that is to say, the fractional function can not be directly converted to the mean inequality, nor can it be directly separated from the constant form Here, the domain of definition of X is not r, so the discriminant method should not be used Big brother, the discriminant method to define the domain must be r The question is how to ask Answer 3L: the definition field is not R. for example, how to find the value field of x = 2 to the power of T?

The method of finding the range of fractional function For the form y = ax ^ 2 + BX + C / ex ^ 2 + FX + G and the function domain is not r (such as x > 0), the general method is to find the range ----------- Note that the general solution, that is to say, the fractional function can not be directly converted to the mean inequality, nor can it be directly separated from the constant form Here, the domain of definition of X is not r, so the discriminant method should not be used Big brother, the discriminant method to define the domain must be r The question is how to ask Answer 3L: the definition field is not R. for example, how to find the value field of x = 2 to the power of T?

1、 Using derivative to solve the problem
After derivation, the denominator is constant and nonnegative, and the numerator is a quadratic function (the cubic term is eliminated), so the problem is easy to solve
2、 It can't be solved by the distribution of the roots of the quadratic equation,
In general, if y = ax ^ 2 + BX + C / ex ^ 2 + FX + G and X ∈ a, a is a subset of R, the function can be changed into the form of F (y) x ^ 2 + G (y) x + U (y) = O. by using the distribution of roots of quadratic equation, the equation can have at least one root on interval a (two cases of having one and two roots on a should be considered)
Attachment: distribution of roots of quadratic equation
The quadratic equation is f (x) = 0, and the quadratic coefficient is positive
The equation has two positive roots
Discriminant > = 0
Axis of symmetry > 0
f(0)>0
2 has two negative roots
Discriminant > = 0
Axis of symmetry 0
Both real roots are greater than k
Discriminant > = 0
Axis of symmetry > k
f(k)>0
Both real roots are less than k
Discriminant > = 0
Axis of symmetry 0
One of 5 is greater than K and the other is less than k
f(k)=0
m0
Only one of the two real roots of the equation is in (m, n)
Discriminant > = 0
f(m)f(n)

The range of the function f (x) = 11 + X2 (x ∈ R) is ()
A. （0，1）B. （0，1]C. [0，1）D. [0，1]

∵ function f (x) = 11 + X2 (x ∈ R), ∵ 1 + x2 ≥ 1, so the range of the original function is (0, 1], so B

Cylinder volume, surface area formula,

The radius of the bottom of the cylinder is r, and the height is h
Volume of cylinder = circumference × square of radius × height
Or cylinder volume = bottom area × height
Letter formula:
V＝Sh
Surface area of cylinder = area of the second base + area of the side
Letter formula:
S table = 2S bottom + s side

A rectangular sports field has a circumference of 270m, and the ratio of length to width is 5:4. What's the area of the sports field,

A rectangular sports field, 270m in circumference, the ratio of length to width is 5:4. The area of this sports field is (4500 square meters)
Formula:
The length is: 270 △ 2 △ 5 + 4 × 5 = 75m
Width: 270 △ 2-75 = 60m
The area is: 75 × 60 = 4500 square meters
Hope to help you!
If you don't understand, please ask. I wish you progress in your study!

Using the rounding method, the accuracy is 0.1, and the approximate value of 5.649 is 0.1______ ．

5.649≈5.6．

A 470 meter long train passes a 1030 meter long bridge in 1 minute and 30 seconds, and then passes a tunnel in 45 seconds at the same speed. How long is the tunnel?
Please write the formula, \ (≥ ▽≤)/~

1030 + 470 = 1500m
1500 △ 90 = 50 / 3 M / s [train speed]
50 / 3 × 45 = 750m
750-470 = 280m

Divide a circle into several equal parts and put it together into a rectangle. The length of the rectangle is 6.28cm. Calculate the area of the circle

The length of a rectangle is half the circumference
The width of a rectangle is the radius of a circle
So the radius of circle = 6.28 △ 3.14 = 2
So area = 3.14 × 2 & # 178; = 12.56

-What is the 100th power of 2 plus the 101st power of - 2?

(-2)^100+(-2)^101=2^100-2^100*2=2^100(1-2)=-2^100

A telecom company has set up two kinds of mobile communication services in the city. The users of type a need to pay a monthly rent of 15 yuan, and then each call takes one minute
If the call time in a month is X minutes, the cost of both a and B is Y1 and Y2 yuan respectively. ① try to express Y1 and Y2 with the algebraic formula containing X. ② when the call time in a month is, Y1 = Y2? ③ according to the call time in a month, which communication service do you think is more favorable?

y1=15+0.1x
y2=0.2x
Y 1 = y 2, x = 150 minutes
One month calls less than 150 minutes, B business benefits;
It's 150 minutes. The two are the same
More than 150 minutes, a business benefits

In trapezoidal ABCD, ad ‖ BC and m are points on ab. if DM bisects angle ADC and cm bisects ∠ BCD, then AD + BC = DC

Take the midpoint F of CD and connect MF (median line), then ad / / MF / / BC
Therefore, ADM = MDF = DMF
So MF = DF
Similarly, MF = CF
Since MF is the median line, AD + BC = 2mf = DF + CF = CD