Compare the sizes of root 5, root 11, root 123

Compare the sizes of root 5, root 11, root 123

The sixth power of radical 5 = 5 & sup3; = 125
The sixth power of the root of the third power 11 = 11 & sup2; = 121
The 6th power of the 6th root 123 = 123
125>123>121
So root number 5 > 6 root number 123 > 3 root number 11

1. Some apples are arranged in a triangle. If there is one apple in the first row, two apples in the second row, four apples in the third row and eight apples in the fourth row, what is their arrangement rule? Guess how many apples are there in the tenth row?
2. There are 30 rows of seats in a cinema. The first row has 25 seats, and each row behind has one more seat than the previous row. Write out the functional relationship between the number of seats in each row m and the number of rows n, and find the value range of the independent variable n

1. Formula: n-1 power of 2
Line 10 has two apples to the power of two
2. Formula: M = 25 + n-1
That is, M = 24 + n (1 ≤ n ≤ 30)

It is known that a and B are monomials of positive integers with coefficients not 1, and the product of a and B is 4x to the third power and y to the second power

There are many
A B
The square of 2x y 2XY
The cubic power of 2x and the square of 2Y
The square of 2x the square of 2XY
2X de 3 power y 2Y

(39 / 12 + 13 / 24) △ 13 / 24
(39 / 12 + 13 / 24) △ 13 / 24 simple method (vertical)
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=(39 of 12 + 13 of 24) × 24 of 13 = 39 of 12 × 24 of 13 + 24 of 13 × 24 of 13 = 6 + 1 = 7

Find f (x) = x / x, when x approaches the left and right limit of 0, and explain whether the limit exists or not

Has the landlord got the wrong number? Is it | x | / x
f(x) = x/x = 1
When x approaches 0, the left and right limits are equal, and the limit exists, which is equal to 1. But when x = 0, it must be defined separately
f(x) = |x|/x
When x > 0, the right limit is 1;
When x < 0, the left limit is - 1
The left and right limits are not equal, and the limit does not exist

Solving equation (3 / 7) * x + 1 = (x + 1) * (7 / 15)

（3/7）*X+1=（X+1）*（7/15）
Then 45x + 105 = 49 (x + 1)
Then 45x + 105 = 49x + 49
Then 56 = 4x
The solution is x = 14

Find the rule: 1 - 17 - 15 31 - 61 () ()
1 -3 7 -15 31 -63 （ ） （ ）
Sorry for the wrong number on it

1,-3,7,-15,31,-63,（127 ）（- 255）.
Law: general term formula
An = 2 ^ n-1, then positive and negative, positive and negative cycle, please adopt in time!

Given the function f (x) = SiNx + TaNx, the arithmetic sequence {an} with 27 items satisfies f (A1) + F (A2) + +F (an) = 0, ask k = how much, f (AK) = 0

SiNx and TaNx are symmetric about the origin in [- 90,90] degrees, so this sequence should be in this interval, so when x is 0 degree, FX is 0, that is, the middle term 14 of 27 items

Definite integral (x + 1) DX / (x ^ 2 + 2x + 2), integrand belongs to - 2 to 0,

∫(- 2→0) (x + 1)/(x² + 2x + 2) dx
= (1/2)∫(- 2→0) (2x + 2)/(x² + 2x + 2) dx
= (1/2)∫(- 2→0) d(x² + 2x + 2)/(x² + 2x + 2)
= (1/2)ln(x² + 2x + 2) |(- 2→0)
= (1/2)ln(2) - (1/2)ln(4 - 4 + 2)
= (1/2)ln(2) - (1/2)ln(2)
= 0

What number should be filled in the blank? The first line is 4 9 20, the second line is 8 5 14, the third line is 10 3, with reasons,
4 9 20
8 5 14
10 3 （ ）
Please give reasons. I also think it's 2, but it seems a bit far fetched.

It can be observed that: the first two numbers add up to 13, and it can be found that: the first number in the first line is 4, the last one is 20, the first number in the second line is 8, the last one is 14, the difference between the first number is 4, the difference between the last number is 6, so when the first number + 2, the last number - 3, so the blank should be filled in 11 or 20 = 4