When x tends to ∞, find the limit of [(x-1 Λ 10) (3x-1)) ^ 10] / (x + 1) Λ20

The answer is obviously 3 ^ 10. When x →∞ (must be ∞, not 0), the limit is 0 if the maximum power of denominator is greater than the maximum power of numerator. If the maximum power of denominator is equal to the maximum power of numerator, the limit is the maximum power coefficient of numerator is greater than the maximum power coefficient of denominator

X tends to infinity (x + 6) / (3x ^ 2 + X + 3) to find limit

The numerator and denominator are divided by X at the same time,
obtain
Original limit
=LIM (x tends to infinity) (1 + 6 / x) / (3x + 1 + 3 / x)
Obviously, 6 / X tends to zero, that is, the molecule tends to constant 1,
And the denominator tends to infinity,
So the limit tends to zero

Why is the limit of 3x-1 8 when x approaches 3

This is very simple, you think so, what is convergence? Convergence means infinitely close, that is, very close to 3, for example, 2.99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999

Two mathematical problems are solved by the equation of one variable and one degree,
1. The distance between the two docks is 72km. It takes 6 hours for a ship to sail downstream and 9 hours for a ship to sail upstream
2. It is every citizen's duty to pay taxes according to law, and citizens with income should pay taxes according to the prescribed tax rate. According to the regulations of 2006, the monthly taxable income is the balance after deducting 1600 yuan from the income. Mr. Li paid 33 yuan of personal income tax in November 2007, so how much is Mr. Li's income in December?
Level monthly taxable income tax rate
1. The part not exceeding 500 yuan 5%
2 500 to 2000 yuan 10%
3. 15% of 2000-5000 yuan portion
4. 20% of the part exceeding 5000 yuan

1. Let the water velocity be X
72/6-X=72/9+X
X = 2, so the speed is 72 / 6-x = 10
2. Suppose that the part of monthly income to be taxed is X. it is estimated that x is between 500 and 2000
（X-500）*10%+500*5%=33
So x = 580
So the income is 1600 + 580 = 2180

One variable linear equation, good additional 100 points
If x and y are rational numbers, and the absolute value of X - x = 0, the absolute value of Y + y = 0, the absolute value of Y is greater than the absolute value of X, the absolute value of X - the absolute value of Y - the absolute value of X + y is reduced

|X | - x = 0 - > | - x | = x - > x > 0 or x = 0
|y|+y=0——>|y|=-y——>y|x|——>x+y|x+y|=-x-y
|x|-|y|-|x+y|=x+y-(-x-y)=x+y+x+y=2x+2y

The speed of train a from place a to place B is 60 km / h, and that of train B from place B to place a is 90 km / h. It is known that a and B are 200 km apart. How far is the place where the two trains meet from place a?

Let two cars meet in X hours. From the question meaning: 60x + 90x = 200, the solution is: x = 43. The place where two cars meet is 60 × 43 = 80 (km) away from A. A: the place where two cars meet is 80 km away from a

A passenger car and a freight car are running opposite each other on the parallel track. It is known that the length of the passenger car is 200 meters, the length of the freight car is 280 meters, and the ratio of the speed of the passenger car to the speed of the freight car is 5:3. It is known that the length of the passenger car is 200 meters, and the length of the freight car is 280 meters
1. The crossing time for the bus to catch up with the truck is one minute,
2. If two cars are running in opposite directions, what is the crossing time?

(1) If the speed of passenger car is x m / min, then the speed of freight car is 0.6 x m / min
（X-0.6X)*1=200+280
X=1200,0.6X=720
A: the speed of the bus is 1200 m / min,
(2) (280 + 200) / (1200 + 720) = 1 / 4 (minutes) = 15 seconds
A: if two cars are driving in opposite directions, their crossing time is 1 / 4 minute

The owner of a shopping mall sells a commodity. He can only sell it at a price no less than 20% of the purchase price. But in order to make more profits, he can price it at a price 80% higher than the purchase price. If you want to buy this commodity with a price of 360 yuan, how much can the price be reduced at most
A. 80 yuan B. 100 yuan C. 120 yuan D. 160 yuan

Let the purchase price of this product be X. according to the meaning of the question, we can get: (1 + 80%) · x = 360, and the solution is: x = 200. The lowest price for profit is 200 × (1 + 20%) = 240, and the shopkeeper can reduce the price by 360-240 = 120 yuan at most

The minimum value of parabola y = 2x & # 178; + 3x + 3 is

y=2x²+3x+3
=2(x+3/4)^2+15/8
The minimum value is 15 / 8

The intersection of parabola y = x & # 178; - 3x + 2 and straight line y = - x + 3 has two points

The intersection of parabola y = x & # 178; - 3x + 2 and straight line y = - x + 3 has X & # 178; - 3x + 2 = - x + 3x & # 178; - 2x + 1 = 2 (x-1) & # 178; = 2x-1 = ± √ 2 when x = 1 + √ 2 or 1 - √ 2, the intersection of parabola and straight line has two

When x tends to ∞, find the limit of [(x-1 Λ 10) (3x-1)) ^ 10] / (x + 1) Λ20