Gerund as subject predicate verb singular and plural Give all the situations and give some examples

Gerund as subject predicate verb singular and plural Give all the situations and give some examples

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When and where lead subject clause predicate verb use singular or plural
What if it's a predicative clause?
eg：the guestion ____ (is /are) when and where they live
Is
If when and where are joined together, use the singular number; if they are separated, use the plural number
When and where they had the party was unknown.
When they had the party and where they had it were unknown.
When and where the factory will be built has been decided
The clause is the subject and the predicate is singular
Use singular numbers, such as:
The house where is near to the lake is my family.
Among them, the first is is the predicate verb of the clause guided by where, and the second is the bathroom verb of the whole main sentence.
Do two subject clauses act as subjects and predicate verbs use singular or plural?
Plural, of course. If you have a subject clause, use the singular
Why is the factorial of 0 equal to 1?
This is a rule, and it doesn't have much specific meaning, but later some formulas may be used, such as differential Taylor polynomials. The first term is f (x) divided by 0! When 0! Must have meaning
If the maximum value of the function y = - X3 + 6x2 + m is 13, then M=______ .
The maximum value of ∵ function y = - X3 + 6x2 + m is 13 ∵ y ′ = - 3x2 + 12x = 0 ∵ x = 0, x = 4, ∵ function increases monotonically on (0,4), decreases monotonically on (4, + ∞), so the answer is: - 19
Why is the factorial of zero equal to one
The teacher didn't explain to us,
This is only a man-made rule, but this man-made rule is not arbitrary. It is based on the factorial operation of positive integers
Because the factorial of n (n is a positive integer) is from 1 × 2 × But this definition is invalid for 0. Then people can only expand the definition according to the factorial relationship of different numbers. From the factorial of positive integers, we can see that (n + 1)! △ n! = n + 1, arbitrary n! = (n + 1)! △ n + 1. Then we can extend this formula to 0 and get 0! = 1! △ 1 = 1 △ 1 = 1
If the function f (x) = x (x-m) 2 has a maximum at x = 2, then the value of the constant M is?
Why not 2?
Derivation of functions
f′（x)=3x^2-4mx+m^2
=(x-m)(3x-m)
Then the extremum appears when x = m and x = m / 3
Suppose there is a maximum when x = M
Then x = 2, M = 2
f(2)f(2+△x)
So if the hypothesis is true, the maximum value will appear when x = m / 3
So m = 6
How to find the factorial of N in MATLAB
prod(1:n)
1. The maximum value of function 6x / (1 + x ^ 2) is
2. F (x) = ax ^ 3-3x + 1 for X ∈ [- 1,1], if f (x) ≥ 0, then a=
1. The function f (x) = 6x / (1 + X & sup2;), F & acute; (x) = [6 (1 + X & sup2;) - 6x * 2x] / (1 + X & sup2;) & sup2; = 6 (1-x & sup2;) / (1 + X & sup2;) & sup2;, let F & acute; (x) = 0 get the stationary point x = ± 1, when x ∈ (- ∞, - 1) ∪ (1, + ∞), F & acute; (x) < 0, f (x) monotonically decreases; when x ∈ (- 1
1 for 6x / (1 + x ^ 2), so that the derivative equals zero
6/（1-x^2)-12x^2/(1+x^2)^2=0
x=±1
Two poles of the function can be obtained
The maximum and minimum can be obtained by substituting x = ± 1
2 f'(x)=3ax^2-3=0
x^2=1/a
According to the meaning of the title, x ^ 2 > = 1
Then 1 / a > = 1
A0
A>0
So 0
If we read "n!" (n is a natural number) as "factorial of n", can the equation (M + n)! = m! + n! Hold for any natural number?
And give an example!
Good words will be added!
Of course not
For example, M = 1, n = 2
Then (M + n)! = 3! = 6
m!+n!=1+2=3
Unequal