The relationship between Lagrange's mean value theorem and Rolle's theorem

The relationship between Lagrange's mean value theorem and Rolle's theorem

Rolle's theorem is a special case of Lagrange's mean value theorem. Lagrange's mean value theorem is a generalization of Rolle's theorem. Uncertainty may also be reversed. For details, refer to the higher number a

1. What is the relationship between Rolle's theorem, Lagrange's mean value theorem and Cauchy's mean value theorem? 2. We know the geometric meaning of Lagrange's mean value theorem
1. What is the relationship between Rolle's theorem, Lagrange's mean value theorem and Cauchy's mean value theorem?
2. What is the geometric meaning of Lagrange mean value theorem?
3. Under what circumstances can we not use the law of lobita to limit?

The denominator function in Cauchy's mean value theorem is x-instant Lagrange's theorem. Cauchy's theorem is the most general, followed by Lagrange's and Rolle's is the most special

The specific heat capacity of water is 4.2 times 10

1kg of water, the heat absorbed (released) is 4.2 times the third power joule of 10 when the temperature increases (decreases) 1 ℃

In the formula F = ma, a is actually the algebraic sum of the acceleration produced by every force acting on the object. Why is it wrong

It's not an algebraic sum, it's a vector sum

Logarithmic function
If a > 0, a ≠ 1, please prove that:
If M = n, then ㏒ am & # 178; = ㏒ an & # 178; is wrong

If it's wrong, just give a counterexample
a>0,a≠1
When m = n = 0, it is meaningless that the position of the true number in ㏒ am ㏒ 178; and ㏒ an ㏒ 178; is 0
The equation doesn't hold, so it's wrong

1/1×2+1/2×3+1/3×4+1/4×5+...+1/39×40

1/1×2+1/2×3+1/3×4+1/4×5+...+1/39×40
=1/1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+...+1/39-1/40
=1-1/40
=39/40

Write all odd and even sums of 1-100 in VB

Private Sub Command1_ Click() dim I, sum1, sum2 as integersum1 = 0sum2 = 0For I = 1 to 100if I mod 2 = 1 then sum1 = sum1 + ielsesum2 = sum2 + iend ifnext iPrint "odd sum" & sum1print "even sum" & sum2end

The value of 1 / 3 + 1 / 15 + 1 / 35 + 1 / 63 + 1 / 99 + 1 / 143 + 1 / 195 + 1 / 255 is a simple algorithm process
There must be an operation process

1/（1x3）+1/（3x5）+1/（5x7）+1/（7x9）+1/（9x11）+1/（11x13）+1/（13x15）+1/（15x17）=(1-2/3)+(2/3-3/5)+(3/5-4/7)+(4/7-5/9)+(5/9-6/11)+(6/11-7/13)+(7/13-8/15)+ (8/15-9/17)＝1-9/17＝8/17...

How much is 2005 4 times 2004 (- 0.25)?

The answer is the power of 2005 of 4 * (- 0.25) the power of 2004 = the power of 2005 of 4 * (- 1 / 4) the power of 2004 = - 4 the power of 2005 / 4 the power of 2004 = - 4

A and B calculate the square of 9-6a + A under the root of a + and get different answers when a = 5
The answer of a is: the original formula = a + radical (A-3) & sup2; = a + A-3 = 2a-3 = 2x5-3 = 7
The answer of B is: the original formula = a + radical (3-A) & sup2; = a + 3-A = 3
Which answer is right? What's wrong with the wrong answer? Why?

A's right
The original formula = a + √ (A-3) & sup2; = a + | A-3|
When a > 3, the original formula = a + A-3 = 2a-3
When A3 = 2a-3 = 7