F (x) = (2x-1) ^ 30 (3x + 2) ^ 20 / (2x + 1) ^ 50, when x approaches ∞, how to find the limit value of the function?

F (x) = (2x-1) ^ 30 (3x + 2) ^ 20 / (2x + 1) ^ 50, when x approaches ∞, how to find the limit value of the function?

f(x)=(2x-1)^30(3x+2)^20/(2x+1)^50
=[(2x-1)/(2x+1)]^30[(3x+2)/(2x+1)]^20
=[(2x+1-2)/(2x+1)]^30[(3x+3/2+1/2)/(2x+1)]^20
=[1-2/(2x+1)]^30[3/2+1/(4x+2)]^20
When x tends to + ∞, 2 / (2x + 1) tends to 0, and 1 / (4x + 2) tends to 0
limf(x)=(1-0)^30(3/2+0)^20=(3/2)^20
x->+∞

Why does limx tend to 0 and sin1 / X not exist
It should be sin (1 / x)

X tends to 0, and 1 / X tends to infinity. At this time, sin1 / X is actually a oscillating function, which may be 1 or - 1. The limit requirement is unique, because there are multiple possible values, so the limit does not exist

A and B both start from a, pass B and drive to C, pass B and drive to C, the distance between AB and BC is equal to the distance between BC. B's speed is 80% of a's speed, B starts 11 minutes earlier than a, but stops at B for 7 minutes, a keeps driving to C, and finally a arrives at C 4 minutes earlier than B. when B starts a few minutes later, a overtakes B

Because 11-7 = 4, the front chase is the same as the later pull,
So it was overtaken by B, and it was overtaken by B after a rest
The time of AB is 80% of that of B
Then the time of B car AB is 4 (1-80%) = 20 minutes
Rest for 7 minutes, that is, 20 + 7 = 27 minutes after B car starts to catch up and exceed

Find the different three digits of each digit so that it is equal to the sum of all the two digits composed of its digits

Let ABC = AB + BC + Ca + Ba + CB + AC = 10A + B + 10B + C + 10C + A + 10B + A + 10C + B + 10A + C = 11 (a + B + C) × 2; so 100A + 10B + C = 11 (a + B + C) × 2, that is, 4b + 7C = 26a, because B ≤ 9, C ≤ 9, so 4B + 7C ≤ 99, that is, 26a ≤ 99, so a = 1 or 2 or 3, when a = 1, 4b + 7C = 26, B = 3, C = 2, when a = 2, 4b + 7C = 52, B = 6, C = 4 When a = 3, 4b + 7C = 78, the solution is b = 9, C = 6, so the three digits satisfying the meaning of the question are 132, 264, 396, and the sum is 132 + 264 + 396 = 792. A: the three digits satisfying the meaning of the question are 132, 264, 396, and the sum is 792

On the map with a scale of 1:6000000, the distance between a and B is 21cm. A train runs from a to B at a speed of 150km / h
How many hours does it take to complete the journey?

First, the actual distance is 21 × 6000000 = 126000000cm = 1260km
Further distance △ speed = time 1260 △ 150 = 8.4 hours

It is known that x > 0, Y > 0

The main rule of basic inequality is that one positive, two definite and three equal, that is, generally positive value can be used; second, it can only be expanded and shrunk when there is a fixed value; of course, both sides of basic inequality can be expanded and shrunk, you can become larger or smaller; third, it can only take the equal sign when two variables are equal
Your topic:
1. Xy = 9 is the fixed value, x > 0, Y > 0 satisfies the positive value;
So: x + 2Y ≥ 2 √ 2XY = 2 √ 18 = 6 √ 2
2. Because 00, meet a positive
Because x + (1-x) = 1 is a fixed value, we can use x + y ≥ 2 √ XY to scale from right to left
So: 2x (1-x) ≤ 2 × [(x + 1-x) / 2] ^ 2 = 1 / 2
If and only if x = 1-x, i.e. x = 1 / 2, take the equal sign

Five sixths of a ton of coal is burned
One ton of coal burns five sixths
Unit 1 is () is () 5 is () unit 1 is () can be associated with:
B is two fifths of A
Unit 1 is () unit 2 is () unit a is () unit 1 is (), which can be associated with:
When water freezes, it expands by one eleventh
Unit 1 is () unit 1 is () unit 11 is () ice volume is () unit 1 is () part

One ton of coal burns five sixths
Unit one is (1 ton of coal) is (6) parts, and unit five is (burned) unit one is (6). It can be thought that there is still one sixth left
B is two fifths of A
Unit 1 is (number a) unit 2 is (number a) unit 1 is (number b) unit 5 is (number a) unit 1 is (number b) unit 5 is (number b) unit 5
When water freezes, it expands by one eleventh
Unit one is (the volume of water), unit one is (more than the original volume), unit eleven is (the volume of water), unit one is (12) and unit one is (11)

The known set a = {x | x ^ 2 + 3x-18 > 0}, B = {x | (x-k) (x-k-1)

The range of a is x > 3 or X

A and B are 360 kilometers apart. A fast train and a local train run from the two stations at the same time and meet each other in 3.6 hours. The speed ratio of the fast train and the local train is 3:2, and the local train is 2

Combined speed 360 / 3.6 = 100 km / h
Express speed 100 * 3 / (3 + 2) = 60 km / h
Slow speed 100-60 = 40 km / h

Solve the two parts of inequality system x-3 + 2 ≥ x + 1, 1-3 (x-1) < 8-x (write integer solution),

（x-3）/2+2≥x+1（1）
1-3（x-1）-2
-1≥x>-2
The integer solution is - 1