The function f (x) = 1 / xsin1 / X is unbounded Why let x = 1 / (2n π + π / 2)? I mean, how can we find such numbers? Why not something else/

The function f (x) = 1 / xsin1 / X is unbounded Why let x = 1 / (2n π + π / 2)? I mean, how can we find such numbers? Why not something else/

Because boundedness is equivalent to the boundedness of the sequence {f (xn)} corresponding to any sequence {xn} whose limit is x0, to prove that there is no boundedness, we need to find a sequence {xn} whose limit is x0, so that {f (xn)} tends to infinity. In this problem, we need to find xn = 1 / (2n π + π / 2) to find such a number, of course, depends on experience

Higher periodic function
Is sin (1-2x) a periodic function? If so, please write the specific steps,

It is a periodic function
sin(1-2X)=-sin(2x-1),
T=2∏/2=∏,
The period is Π

Is high number a periodic function?
Is f (x) = sin (x ^ 2) a periodic function?

If the period is t
f(x+T)-f(x)=
sin(x^2+2xT+T^2)-sin(x^2)
=2cos(x^2+2xT+T^2)sin(2xT+T^2)=0
Cos (x ^ 2 + 2XT + T ^ 2) = 0 or sin (2XT + T ^ 2) = 0 for any X
Only t = 0 is satisfied
So it's not a periodic function

Fill - 1, - 2,3, - 4, - 5,6, - 7, - 8,9 in the large square composed of nine small squares, so that each row, each column, and each column is
Fill - 1, - 2,3, - 4, - 5,6, - 7, - 8,9 in the big positive of nine small squares, so that the product of each row, column and diagonal is positive!

3 -1 -2
-5 6 -4
-7 -8 9

There are four cylindrical columns in the corridor outside the classroom. The diameter of the bottom of each column is 6 decimeters. Paint these columns with 0.3 paint per square meter
How many kilos of paint are needed? The number should be kept to 2 decimal places

When r = 0.3m, H = 3M and S = 5.655, the total area of the cylinder is 4 * 5.655 = 22.62
0.3*22.62=6.79

Use appropriate operation symbols to make - 4,3,8,1 operation result 24
emergency

[8-(-4)]*(3-1)

Z = x2 + Y2, X2 + 2Y2 + 3z2 = 4 for dy / DX, DZ / DX

Z = x2 + Y2 (1) x2 + 2Y2 + 3z2 = 4 (2) if both sides of X are derived, then DZ / DX = 2x + 2ydy / DX (3) if both sides of X are derived, then 2x + 4ydy / DX + 6zdz / DX = 0 (4) if both sides of X are substituted into 4, then 2x + 4ydy / DX + 6Z (2x + 2ydy / DX) = 0x + 2ydy / DX + 6Z (x + YDY / DX) = 0 (2Y + 6yz) dy / DX = - x-6xzdy / DX = (- x-6xz) / (2Y + 6yz)

Calculation: 1 + 2 + 3 + +2002+2003+2002+… +3+2+1=______ ．

1+2+3+… +2002+2003+2002+… +3 + 2 + 1 = (1 + 2002) × 2002 △ 2 × 2 + 2003 = 2003 × 2002 + 2003 = 2003 × (2002 + 1) = 20032

How many different denominations can be made up of one dime, two dimes and five dimes, three one yuan and three five yuan
Take analysis
Any combination will do
How many different currencies can be formed

2 × 2 × 2 × 4 × 4-1 = 127 species
There are one dime, two dimes and five dimes, and there are two ways to choose them,
There are three pieces of one yuan and five yuan, which can be divided into four types: 0, 1, 2 and 3
We don't take all five. This is not included, so we need to take them out

Is the bisector of quadrant 2.4 axisymmetric or centrosymmetric about the origin

On the centrosymmetry of the origin