Prove that the limit of binary function does not exist?

Multiplication of numerator and denominator
Radical (XY + 1) + 1
The molecule becomes (XY + 1) - 1 = XY
Lim radical (XY + 1) + 1 = 1
So the original formula = lim... XY / (x + y)
Then, you can turn down the numerator xy and denominator, and the original formula becomes
lim 1/ (1/x+1/y)
So it can be done

How to prove the continuity of partial derivative of binary function

Generally, it is a piecewise function. The partial derivative can be obtained directly from the continuous and differentiable segment of the open interval, and then the partial derivative value of the segment point can be obtained by using the definition method, or it can be judged that it does not exist. Thus, the continuity of the partial derivative at the segment point can be judged

For the image of the equation of higher degree in one variable, (x + 2) (x-1) (X-5), please draw it and tell me how to draw the axis!

Let f (x) = (x + 2) (x-1) (X-5), then f (x) = 0 has three x = - 2 or 1 or 5, so f (x) must pass (- 2,0), (1,0), (5,0), and then substitute x = 0 to get f (x) = 5 > 0, so f (x) increases before - 2, - 2 to 1 is an upper convex function, 1 to 5 is lower convex, and 5 increases after

The unknown?
8 is 27 less than 7% of a number. Find the number

This number is X
8=x*7% -27
x*7%=35
x=500

When n → infinity, Lim {2 ^ n times sin (x / 2 ^ n)}
X is not zero constant
The process of problem solving is more specific!!!

x.
When m is large enough, 1 / M and sin (1 / M) tend to be equal
Finally, when n tends to infinity, 2 ^ n times X / 2 ^ n is X

11+22+33+44… What is the remainder of the sum of 2007 * 2007 + 2008 * 2008 divided by 7?

You can divide every seven of the original expressions into a group. First, look at the first group: 1 + 4 + 9 + 16 + 25 + 36 (+ 49). Because the remainder of the last number divided by 7 is 0, it can be rounded off. The first six add up to 91, and the remainder of 7 is 0. Then look at the second group, which can be written as: (7 + 1) ^ 2 + (7 + 2) ^ 2 + (7 + 3) ^ 2 + (7 + 4) ^ 2 + (7 + 5) ^

Simple operation: 13 × (- 2 / 3) + 0.34 × (- 2 / 7)
13×（-2/3）+0.34×（-2/7）-1/3×13+（-0.34）×（-9/7）

Original formula = 13 × (- 2 / 3-1 / 3) + 0.34 × (- 2 / 7 + 9 / 7)
=13×（-1）+0.34×1
=-13+0.34
=-12.66

Solving process of differential equation y '' - 4Y '= 5, y (0) = 1, y' (0) = 0

The characteristic equation of the homogeneous equation y '' - 4Y '= 0 is R & sup2; - 4R = 0, then the characteristic root is R1 = 0, R2 = 4
The general solution of the homogeneous equation y '' - 4Y '= 0 is y = C1E ^ (4x) + C2 (C1, C2 are integral constants)
Let a solution of the equation y '' - 4Y '= 5 be y = ax
∵ y '= a, y' '= 0. Substituting into the original equation, - 4A = 5 = = > A = - 5 / 4
A special solution of the equation y '' - 4Y '= 5 is y = - 5x / 4
The general solution of the equation y '' - 4Y '= 5 is y = C1E ^ (4x) + c2-5x / 4 (C1, C2 are integral constants)
∵y(0)=1,y'(0)=0 ==>C1+C2=1,4C1-5/4=0
∴C1=5/16,C2=11/16
So the solution of the equation y '' - 4Y '= 5 satisfying the initial condition is y = [5E ^ (4x) + 11] / 16-5x / 4

How many liters is one cubic meter of water
Specific gravity: the weight of a unit volume of material. Specific gravity of water: the weight of a single volume of water. Specific gravity of pure fresh water: γ = 1g / cubic centimeter = 1kg / cubic decimeter = 1t / m3. "How many tons is one cubic centimeter of water equal to?" 1 cubic centimeter (= 1 / 1000L) of water weighs 1g = (1 / 1000000) tons, 1 cubic decimeter (= 1L) of water weighs 1kg = (1 / 1000t), 1 cubic meter (= 1000L) of water weighs 1t You can also learn {how many liters is a cubic meter of water equal to?}

One liter of water equals two Jin

Prove that the limit of binary function does not exist?