What's the use of local boundedness of function limits What's the use of this theorem? To prove inequality? To prove extremum? To prove local continuity? What's the use?

What's the use of local boundedness of function limits What's the use of this theorem? To prove inequality? To prove extremum? To prove local continuity? What's the use?

Local boundedness of function limit, a property of function limit,
As for the role, for example:
Just like "the sum of the two sides of a triangle is greater than the third side", what do you think is the use of this property?
What's the use of the uniqueness of function limit?
The purpose of these properties is to understand and understand the characteristics of function limit. As a property of function limit, it can also deduce other properties about function limit, but in most cases it is not a sufficient condition
As for the three usages you mentioned, they vary from topic to topic

a^2-ab+b^2/a^3+b^3
We should make an appointment

(a^2-ab+b^2)/(a^3+b^3)
=(a^2-ab+b^2)/[(a+b)(a^2-ab+b^2)]
=1/(a+b)

If X1 and X2 are two of the quadratic equations x ^ 2-3x-1 = 0, then X1 ^ 3 + x2 ^ 3=

If X1 and X2 are two of the quadratic equations x ^ 2-3x-1 = 0, then
x1+x2 = 3
x1x2 = -1
∴ x1³+x2³ = (x1+x2)(x1²+x1x2+x2²)
= 3[(x1+x2)²-x1x2]
= 3×(3²+1)
= 30

X + 5 / 11 = 7 / 9

X + 5 / 11 = 7 / 9 double 99
99x+45=77
99x=77-45
99x=32
x=32/99

There is a column of numbers A1, A2, A3, A4. An. Starting from the second number, each number is equal to the difference between 1 and the reciprocal of the number before it. A1 = - 1 / 2
1, find the size of A1 and A2009
2, find the value of a1 + A2 + a3 +. A16

The problem can be transformed into an = 1 - 1 / (an - 1), which is a problem of finding the general term of a sequence of numbers

What about equation 21 x = 6

Divide both sides of the equation by 21 to get x = 6 / 21 = 2 / 7

Operation research standard min z = 2x1 + x2-5x3-x4
st :3x1+X4=5
two

No decision condition, no truth -- if all ≥ 0, the result is (you wrote the last line wrong)
max(-z)=-2x1 -x2 +5x3+x4
3x1 +x4 +x5=25
x1 +x2 +x3 +x4=20
4x1 +6x3 -x6=5

Given (x + 4) (3x-2) = 3x & # 178; + 10x-8, the factorization 3x & # 178; + 10x-8 is equal to

3x²+10x-8
=(x+4)(3x-2)

As shown in the figure, De is the median line of △ ABC, M is the midpoint of De, and the extension line of CM intersects AB at point n, then s △ DMN: s quadrilateral anme equals ()
A. 1：5B. 1：4C. 2：5D. 2：7

∵ De is the median line of △ ABC, ∵ de ∥ BC, de = 12bc. If the area of △ ABC is 1, according to de ∥ BC, ∥ ade ∥ ABC, ∥ s ∥ ade = 14, am is connected. According to the title, s ∥ ADM = 12S ∥ ade = 18S ∥ ABC = 18, ∥ de ∥ BC, DM = 14bc, ∥ DN = 14bn, ∥ DN = 13bd = 13ad. ∥ s ∥ DNM = 13s ∥ ADM = 124, ∥ s quadrilateral anme = 14 − 124 = 524, ∥ s ∥ DMN: s quadrilateral anme = 124:524 =1: 5. So a

Determine the number of integers of known number, and subtract () from the number of integers is equal to 10 times

The number of digits of an integer minus one is the number of times ten