Find the monotone interval of function FX = - x ^ 2 + | x | and find the maximum and minimum value of function y = FX on [- 1,2]

Find the monotone interval of function FX = - x ^ 2 + | x | and find the maximum and minimum value of function y = FX on [- 1,2]

-1≤x

The period, maximum and minimum of the function y = 3sin (2x + π / 3)

y=3sin(2x＋π/3)
1. The minimum positive period is 2 π / 2 = π
2. The maximum is 3 and the minimum is - 3

Calculating determinant - a 1, a 10... 000 - a 2, a 2... 00.000. - an an 11... 11

-a1 a1 0 ...0 0
0 -a2 a2 ...0 0
.........
0 0 0 ...-an an
1 1 1 ...1 1
Add 2,3,..., n columns to the first column, and the result is
0 a1 0 ...0 0
0 -a2 a2 ...0 0
.........
0 0 0 ...-an an
n+1 1 1 ...1 1
Expand by column 1
Determinant = (n + 1) * (- 1) ^ n * A1A2... An

12+2/7x=68

12+2/7x=68
12+2/7x-12=68-12
2/7x=56
x=56*7/2
x=196

A barrel of oil weighs 860 kg. After 80% of the oil in the barrel is used, the barrel weighs 180 kg. How many kg is the empty barrel?
(1) A barrel of oil weighs 860 kg. After 80% of the oil in the barrel is used, the barrel weighs 180 kg. How many kg is the empty barrel?
(2) This year, an electrical factory will produce 4800 tape recorders, 1 / 5 more than planned. How many more?
(3) A batch of cement is planned to be produced in 12 days for workshop a and 15 days for workshop B. the two workshops produce together for 7 days, exceeding 42 tons. How many tons of cement is planned to be produced?
(4) Four children buy a 60 yuan boat together. The first child pays half of the total amount paid by other children, the second child pays one third of the total amount paid by other children, and the third child pays one fourth of the total amount paid by other children. How much does the fourth child pay?

1. X + y = 860 0.8x + y = 180 x = 850 y = 102. 4800 / 1.2 = 4000 3. Suppose the total amount of work is 1. Party A and Party B work together for one day is 1 / 12 + 1 / 15 = 9 / 60 7 days to do 63 / 60 more than 1 / 20 total amount = 8404. The first child: 60 / (1 + 1 / 2) * 1 / 2 = 20 the second: 60 / (1 + 1 / 3) * 1 / 3 = 15 the third

On the proof of continuity and differentiability of function!
1、 Judge whether f (x) is continuous at x0
(version 1)
1. The existence of F (x0)
2. LIM (x) tends to x0 and f (x) exists
3. When the first two exist, f (x0) = LIM (x tends to x0) f (x)
(version 2)
1. The existence of F (x0)
2. LIM (x) tends to x0 + F (x) exists
3. LIM (x tends to x0 -) f (x) exists
4. LIM (x tends to x0 +) f (x) = LIM (x tends to x0 -) f (x) = f (x)
Which is right
2、 Judge whether f (x) is continuous on [a, b]:
1. Any point on (a, b) is continuous
2. Right continuous on a, left continuous on B (how to prove this? LIM (x tends to a +) = LIM (x tends to a))
3、 Judge the differentiability of function at some point x0
Is it necessary to prove that f (x) is continuous at x0?

1、 If the limit at a certain point exists, then the left and right limits must exist and be equal
2、 No, let's take a counter example. For example, if there is no definition at a and B, we need to prove whether it is continuous according to the definition. If any point in (a, b) is continuous, then any point in (a, b) is continuous
3、 It is not necessary to be continuous
I suggest you strengthen the understanding of the definition of limit, continuity and derivability!

VB topic, expression ABS (- 5) * 5 / 5 value calculation process

*Highest priority, then to / and then to\
Equivalent to (ABS (- 5) * 5) \ (5 / 5)
=(5*5)\1
=25

What are the two groups of sentences that can reflect the characteristics of summer flow in the Three Gorges

As for Xia Shuixiang mausoleum, it's blocked along the trace,
Sometimes the king sent the White Emperor to Jiangling at dusk. During that time, although he rode to the wind, he was not ill

From the relation between limit and infinitesimal, f (x) sin2x = ((2 + a) 3x ^ 2 + 1) ^ 2 - 1, when x → 0, → 0
How does f (x) sin2x = ((2 + a) 3x ^ 2 + 1) ^ 2 - 1 come from

When Lim x → 0 [(1 + F (x) sin2x) ^ 1 / 2 - 1] / [e ^ (3x ^ 2) - 1]
Change the denominator equivalent infinitesimal to 3x ^ 2
The limit of the original problem is given = 2
Find f (x) / X when Lim x → 0
Lim x → 0 [(1 + F (x) sin2x) ^ 1 / 2 - 1] / [e ^ (3x ^ 2) - 1]
Replace the numerator and denominator with the equivalent infinitesimal
=lim (x→0)f(x)sin2x/(3x^2)
=lim (x→0)f(x)2x/(3x^2)
=lim (x→0)f(x)2/(3x)
=2
So f (x) = 3x
So LIM (x → 0) f (x) / X
=lim （x→0）3x/x
=3

There are 4 boys less than 59 students in a class and 6 girls more than 40% of the class
A. 5B. 3C. 9D. 10

Class: (6-4) △ 1-59-40%) = 2 △ 245, = 45 (people); boys: 45 × 59-4 = 25-4 = 21 (people); boys are less than girls: 45-21-21 = 3 (people); answer: boys are less than girls by 3