Let the tangent of the curve y = AX2 at point (1, a) be parallel to the straight line 2x-y-6 = 0, then the value of a is______ ．

Let the tangent of the curve y = AX2 at point (1, a) be parallel to the straight line 2x-y-6 = 0, then the value of a is______ ．

Y '= 2aX, then the slope of the tangent k = y' | x = 1 = 2A, ∵ the tangent is parallel to the straight line 2x-y-6 = 0 ∵ 2A = 2 ∵ a = 1, so the answer is 1

Reading comprehension: calculate the value of (x + y) (x-2y) - my (nx-y) (M and N are constants). When substituting the value of X and Y into the calculation, careless Xiaoming and Xiaoliang misjudged the value of Y, but the result was equal to 25. Careful Xiaomin substituted the correct value of X and Y into the calculation, and the result was just 25. In order to find out, she randomly changed the value of Y into 2006, (1) according to the above situation, try to explore the mystery; (2) can you determine the value of M, N and X?

(1) ∵ (x + y) (x-2y) - my (nx-y) = X2 - (1 + Mn) XY + (m-2) Y2, and the original formula has nothing to do with the value of Y, we can judge that m-2 = 0, (1 + Mn) = 0. In this case, the value of the original formula = x2 has nothing to do with the value of Y. (2) because the value of the original formula has nothing to do with the value of Y, so m-2 = 0, M = 2, (1 + Mn) = 0, n = - 12

Finding limit with pinch theorem
limn[1/(n^2+π)+1/(n^2+2π)…… +1/(n^2+nπ)]=1

n*n/(n^2+π)

In calculating the value of (x + y) (x-2y) - my (nx-y) (m, n are constants), when the value of X and Y is substituted into the calculation
Careless Xiaoming and Xiaoliang misjudge the value of Y, but the result is equal to 25. Careful Xiaomin substitutes the correct values of X and Y into the calculation, and the result is just 25. In order to explore, she randomly changes the value of Y into 2012. Do you think it's strange, but the result is still 25
(1) According to the above, try to explore the mystery
(2) Can you determine the values of M, N and X?

(1) It is shown that the simplified formula has nothing to do with y
(2) Yes
The original formula = x ^ 2-xy-2y ^ 2-mnxy + my ^ 2 = x ^ 2 - (1 + Mn) XY + (m-2) y ^ 2,
If y = - 2, then y = - 1
And the original formula = x ^ 2 = 25, so x = plus or minus 5

Who can explain the pinch theorem step by step?
Pinch theorem is particularly difficult to master, who knows how to quickly solve the problem of pinch theorem

The thinking of pinch method is to enlarge and reduce
Step one, zoom in
Enlarge and transform the given limit formula to get the limit value
The second step is to narrow down
The given limit formula is reduced and transformed to get the limit value
The third step is to get the value of the limit by the pinch theorem
The simple point is that the two limits are enlarged and reduced by changing
The limit value of enlargement and reduction is equal. The limit value is obtained by the pinch theorem

X ^ n + x ^ n-1y + x ^ n-2y ^ 2 +. + x ^ 2Y ^ n-2 + XY ^ n-1 + y ^ n = how much?

I'm sorry. I just know
（x-y）（x^n+x^n-1y+x^n-2y^2+.+x^2y^n-2 +xy^n-1 +y^n）
=x^(n+1)-y^(n+1)
Then x ^ n + x ^ n-1y + x ^ n-2y ^ 2 +. + x ^ 2Y ^ n-2 + XY ^ n-1 + y ^ n
=x^(n+1)-y^(n+1)/（x-y)

It is proved that LIM (x → a) f (x) = 0 LIM (x → a) f (x) = 0

It is proved that: (1) necessity, ∵ LIM (x - > A) │ f (x) │ = 0
For any ε > 0, there is always a > 0, when 00, when 0

Calculation: 3 (Y-Z) - 2Y + Z (Z + 2Y)

Original formula = 3y-3z - (4y2-z2)
=3y-3Z-4y2+Z2

What does math Lim mean

Limit

Calculate (2Y + 1) ^ 2 × (2Y + 1) ^ 3 + (2Y + 1) ^ 4 [- (2Y + 1)]

(2y+1)^2×(2y+1)^3+(2y+1)^4【-(2y+1)】
=(2y+1)^5 - (2y+1)^5
=0