Is there a difference between a great many and a great many of?

Is there a difference between a great many and a great many of?

A great many + n
A great many of + n
A great number of is a pronoun phrase followed by a countable noun
The difference between a great many and a great many of
The difference between a great many and a great many of
If you don't have a determiner, use the former. If you do, use the latter
a great many books
a great many of the books
The difference between a great deal and a great deal of
The former is used as adverbial and the latter as attribute to modify noun
A great many people
A great many of the people
A great many of us
A great deal of water
He is a great deal taller than me.
Here a great deal is an adverb of degree.
A great many + n
A great many of + n
A great deal
A great deal of
I hope I can help you
A great deal, a great many.
This pair of phrases both mean "many" and "a large number". There is no difference in meaning, but mainly in usage.
A great deal is often used with uncountable nouns; a great many is used with the plural form of countable nouns, and their differences are the same as those of many and many.
When a great deal is followed by a noun, of: a great many is added
A great deal, a great many.
This pair of phrases both mean "many" and "a large number". There is no difference in meaning, but mainly in usage.
A great deal is often used with uncountable nouns; a great many is used with the plural form of countable nouns, and their differences are the same as those of many and many.
When a great deal is followed by a noun, of: a great many is used instead of of of a great deal (or many) and a good deal (or many), but the tone of the former is heavier than that of the latter. A great (or good) deal is often used instead of a great (or good) deal in spoken English.
Example:
As the new year is approaching, we have a great deal of preparation work to do.
With the coming of the new year, we have a lot of preparation to do.
The High Island Reservoir can store a great deal of water.
Wanyi reservoir can store a lot of water.
There are a great many trees and folwers in the botanical garden.
There are many trees and flowers in the botanical park. Put it away
The difference between a great many and a great deal and a good deal of and a lot of
A great many modify countable
A great deal of and a good deal of
A lot of both
How to find the left and right limit of function
What are the left and right limits of y = 1 / {1-e ^ [x / (1-x)]} when x = 0?
X -- > 0 -, Y -- > positive infinity
X -- > 0 +, Y -- > negative infinity
Given the set a = {1, 2, 3, 4, 5}, B = {(x, y) | x ∈ a, y ∈ a, X-Y ∈ a}, then the number of elements in B is ()
A. 3B. 6C. 8D. 10
From the topic meaning, when x = 5, y = 1, 2, 3, 4, x = 4, y = 1, 2, 3, x = 3, y = 1, 2, x = 2, y = 1 to sum up, the number of elements in B is 10, so D is selected
It is known that the domain set of function f (x) = √ (x + 1) / (X-2) is a, and function g (x) = LG {x ^ 2 - (2a + 1) + A ^ 2+
It is known that the domain set of function f (x) = √ (x + 1) / (X-2) is a, and the domain set of function g (x) = LG {x ^ 2 - (2a + 1) + A ^ 2 + a} is B
10 - 14 days and 23 hours to the end of the problem
It is known that the domain set of function f (x) = √ (x + 1) / (X-2) is a, and the domain set of function g (x) = LG {x ^ 2 - (2a + 1) + A ^ 2 + a} is B
Finding sets a and B
If a ∪ B = B, find the value range of real number a
From x + 1 ≥ 0
      x-2≠0
&The solution is x ≥ - 1 and X-2 ≠ 0,
&So a = [- 1,2) ∪ (2, ∞)
&By x ^ 2 - (2a + 1) x + A ^ 2 + A & gt; 0
     （x-a）[x-(a+1)]>0
&The solution is X & lt; a or X & gt; a + 1
&So B = (∞, a) ∪ (a + 1, ∞)
  
&Nbsp; & nbsp; & nbsp; a ∪ B = B, indicating that a is contained in B,
&So & lt; & nbsp; - 1;
(the second question uses the combination of number and shape to express the interval range of a and B, as shown in the figure, it is easy to get a + 1 & lt; - 1, & nbsp; to do this type of problem, we should pay special attention to whether we can take the equal sign.)
On the solution of left and right limit of function
Piecewise function
y=x-1 x0
Is f (x) continuous at x = 0?
For y = X-1, X belongs to rational number, and is continuous in the whole definition interval, so it is also continuous at x = 0. So Lim O + = Lim 0 - = f (0) so we can find the left limit of F (x) at 0.
The left limit of the piecewise function is - 1.
In conclusion, for such a class of piecewise functions, for a certain function, for example, y = X-1, X
The conditions of continuity are as follows: 1. The left limit and the right limit of a function at a given point exist at the same time and are equal; 2. The limit value of a function at a given point must be equal to the value of the function at this point; other factors need not be considered
That's OK.
1、 For y = X-1, X belongs to rational number, which is continuous in the whole definition interval (here we should consider that x belongs to all real numbers, only rational number is not enough);
2、 In this problem, the left limit Lim 0 - = 0-1 = - 1, because y = X-1 is left continuous at x = 0 (of course y = X-1 is continuous on all real numbers), so it can be directly substituted. ... unfold
That's OK.
1、 It is impossible for the entire interval to be rational (x = 1);
2、 In this problem, the left limit Lim 0 - = 0-1 = - 1, because y = X-1 is left continuous at x = 0 (of course y = X-1 is continuous on all real numbers), so it can be directly substituted. Put it away
Given that the set a = {X / kx2-8x + 16 = 0} has only one element, try to find the value of the real number k, and use the enumeration method to represent the set a
If there is only one element, the equation has only one solution
K = 0, then - 8x + 16 = 0, x = 2
If K ≠ 0 is a quadratic equation of one variable, then the discriminant is equal to 0
64-64k=0,k=1
Then x & sup2; - 8x + 16 = 0, (x-4) = 0
X=4
So k = 0, k = 1
A = {2} or a = {4}
△=b^2-4ac=8^2-4*k*16=0
The solution is k = 1
X=4
So a = {4}
Let f (x) = LG2 + x2 − x, then the domain of F (x2) + F (2x) is______ .
To make the function meaningful, then 2 + x2 − x ＞ 0, the solution is x ∈ (- 2,2) f (x2) + F (2x). To ensure that both formulas are meaningful, then − 2 ＜ x2 ＜ 2 − 2 ＜ 2x ＜ & nbsp; 2 {x ∈ (- 4, - 1) ∪ (1,4), so the answer is: (- 4, - 1) ∪ (1,4)
Finding the left and right limit of function
The original problem is as follows: x = 0 is () of arctan (1 / x)
1. The second kind of discontinuity 2, can go to the discontinuity 3, jump discontinuity
It is said that the left and right limits are not equal, but I will not seek them
How to find out the equation of π / 2?
Candidate C
When x tends to 0 +, 1 / X tends to + infinity, limarctan (1 / x) = Pie / 2
When x tends to 0 -, / X tends to - infinity, limarctan (1 / x) = - Pie / 2
Then the two limits are not equal, which is the break point between jumps
limarctan(1/x)=-π/2
x→0-
limarctan(1/x)=π/2
x→0+
Because the left and right limits exist and are not equal
So x = 0 is the breakpoint between jumps