English words or phrases to express gratitude for example:thank you ,acknoledgement……

English words or phrases to express gratitude for example:thank you ,acknoledgement……

gratitude
I would appeciate it if......
It's so nice of you .....
I'd appreciate it if....
In fact, the most useful is the simplest, as long as you can use it. I think it's very useful:
thank you for sth
For example:
thank you for your help
thank you for your gift
thank you for your conscientious service
thank you for your immediate attetion.
and so on
Your favorite English words or phrases
To have a deep artistic conception
P. S. I'm talking about words=_ =|||
It's not a sentence
I like it best. It means silence
it's my life
very well
You know what
You get it!
So what!
Desprado!
To be or not to be, thhat's a problem.
Shakespeare
enjoy yourself
be good , do right!
the more the better
HAPPY
Words and phrases in English for "now, now"
As the title
Just now "I do my home work just now." I'll do my homework at once“
I go to school at once“
at once
just now；now
at the monent
at this moment
at present
current
now/nowadays
Given the parabola y = MX & # 178; - 2 (3m-1) x + 9m-1, no matter what the value of X is, the value of function y is non negative, and the value range of M is obtained
M>0
△=4(3m-1)²-4m(9m-1)=1/5
The monotone increasing interval of function f (x) = Log1 / 2 (- X & # 178; - x + 2) is?
Domain of definition
-x²-x+2>0 ==> x²+x-2
f(X)=㏒1/2↑［-(X+1/2)^2+7/4］
From - (x + 1 / 2) ^ 2 + 7 / 4 > 0: (- 1 - √ 7) / 2
As shown in the figure, point C is on the number axis, and AC: BC = 1:5, find the number corresponding to point C. (because ∵ so ∵) a B -- → - 10 14
Because AC: BC = 1:5, BC is longer than AC
14-（-10）=24
Using proportional knowledge:
24 divided by (1 + 5) = 4
-10 + 1 times 4 = - 6
A: the corresponding number of point C is - 6
Let f (x) = {| lgx |, x > 0 - x ^ 2-2x, x > 0 - x ^ 2-2x
Let 2F & # 178; (x) - 3f (x) + 1 = 0
The solution is f (x) = 1, or F (x) = 1 / 2
The image of F (x) is shown in the figure above. Make two lines y = 1 and y = 1 / 2, and the intersection points with F (x) are 3 and 4 respectively
So there are seven zeros
Find the maximum value of function f (x) = - (Log1 / 2 (x)) ^ 2-log1 / 4 (x + 5) in the range of 2 ≤ x ≤ 4
There is something wrong with your input, so you can't solve it. Find the maximum value of the function f (x) = - (Log1 / 2 (x)) ^ 2-log1 / 4 (x) + 5 in the range of 2 ≤ x ≤ 4. Let t = log0.5 (x) t ∈ [- 2, - 1] y = - T & # 178; - t / 2 + 5 = - (T + 1 / 4) &# 178; + 81 / 16 symmetry axis t = - 1 / 4, image opening downward
On the number axis, the numbers corresponding to points a and B are respectively a and B, and | a + 10 | and (B-14) are opposite trees. Point C on the number axis satisfies AC: BC = 1:5
(1) If a, B and C start from a and B at the same time and want to move, they have moved 3 units more than a per second, and they meet at 2 units from the origin,
1. | a = 10 | + (B-14) ^ 2 = 0, because the sum of non negative numbers is 0, and each of them is 0, so a = - 10 b = 14. Let C correspond to x, then 14-x = 5 | - 10-x |, so x = - 6 or - 16 2. Let a move m units per second, then B move (M + 3) units, then (10-2) / M = (14 + 2) / (M + 3) or (10 + 2) / M = (14-2) / (M +
It is known that the function f (x) is monotone in its domain of definition
Suppose there are two unequal zeros x1, X2, let x2 > x1, and f (x) be a monotone increasing function
Then f (x2) = f (x1) = 0
But since f (x) is a monotone increasing function, according to x2 > x1, f (x2) > F (x1)
contradiction
So f (x) has at most one zero point