Translation of proper nouns in mathematics into English

Translation of proper nouns in mathematics into English

Mathematics, maths (BRE), math (AME) axiom axiom theorem calculation calculation operation prove prove prove prove hypothesis hypothesis hypothesis proposition arithmetic plus (prep.), add (v.), ad

How to express mathematical proper nouns in Higher Mathematics?
Sequence, limit, derivative, differential, integral, constant, series, power series, double integral, etc!
How to solve the problem of advanced mathematics in English?
Who can tell me the English expression of mathematical terms in advanced mathematics 4? And how to solve problems in English?

Sequence is sequence
The limit is limit
Derivative is derivative
Differential is differential
Integral is integral
Constant
Series
Power series
Double integral
Don't worry, the symbols are the same. Pay attention to the key words

What is the relationship between limit continuous derivatives?
Can you be more specific

Limit, continuity and differentiability are necessary and not sufficient conditions
That is: the limit is not necessarily continuous, continuous limit must exist

What are the mathematical formulas of senior two?

Vector formula:
1. Unit vector: unit vector A0 = vector A / | vector a|
2. P (x, y) then vector OP = x vector I + y vector J
|Vector op | = root sign (x square + y Square)
3.P1(x1,y1) P2(x2,y2)
So vector p1p2 = {x2-x1, y2-y1}
|Vector p1p2 | = radical [(x2-x1) square + (y2-y1) square]
4. Vector a = {x1, X2} vector b = {X2, Y2}
Vector a * vector b = | vector a | * | vector B | * cos α = x1x2 + y1y2
Cos α = vector a * vector B / | vector a | * | vector b|
(x1x2+y1y2)
= ————————————————————
Radical (x1 square + Y1 Square) * radical (x2 square + Y2 Square)
5. Space vector: the same as above
(hint: vector a = {x, y, Z})
6. Necessary and sufficient conditions:
If vector a ⊥ vector b
So vector a * vector b = 0
If vector A / / vector b
Then vector a * vector b = ± | vector a | * | vector B|
Or X1 / x2 = Y1 / Y2
7. | vector a ± vector B | squared
=|Vector a | square + | vector B | square ± 2 vector a * vector b
=(vector a ± vector b) squared
Trigonometric function formula:
1. Universal formula
Let Tan (A / 2) = t
sina=2t/(1+t^2)
cosa=(1-t^2)/(1+t^2)
tana=2t/(1-t^2)
2. Auxiliary angle formula
asint+bcost=(a^2+b^2)^(1/2)sin(t+r)
cosr=a/[(a^2+b^2)^(1/2)]
sinr=b/[(a^2+b^2)^(1/2)]
tanr=b/a
3. Triple angle formula
sin(3a)=3sina-4(sina)^3
cos(3a)=4(cosa)^3-3cosa
tan(3a)=[3tana-(tana)^3]/[1-3(tana^2)]
4. Integration and difference
sina*cosb=[sin(a+b)+sin(a-b)]/2
cosa*sinb=[sin(a+b)-sin(a-b)]/2
cosa*cosb=[cos(a+b)+cos(a-b)]/2
sina*sinb=-[cos(a+b)-cos(a-b)]/2
5. Integration and difference
sina+sinb=2sin[(a+b)/2]cos[(a-b)/2]
sina-sinb=2sin[(a-b)/2]cos[(a+b)/2]
cosa+cosb=2cos[(a+b)/2]cos[(a-b)/2]
cosa-cosb=-2sin[(a+b)/2]sin[(a-b)/2]

It is proved that the sum of the second partial derivatives of X, y, Z in U = Z arctan (x / y) is 0
The main reason is that the partial derivatives of y can't be found together,

u'x= z/(1+x^2/y^2)* 1/y=zy/(x^2+y^2)
u'y=z/(1+x^2/y^2)* (-x/y^2)=-zx/(x^2+y^2)
u'z=arctan(x/y)
u"xx=-2xyz/(x^2+y^2)^2
u"yy=2xyz/(x^2+y^2)/^2
u"zz=0
So u "XX + U" YY + U "ZZ = 0

If x + X + X + y + y = 54, x + X + y + y = 56, then x=______ ，y=______ ．

Because x + X + X + y + y = 54, x + X + y + y = 56, 2, 1 × 2 - 2 × 3, 6x + 4y-6x-9y = 108-168, 5Y = 60, y = 12; because x + X + X + y + y = 54, 3x = 54-24, x = 10

Why is a fraction divided by a number equal to multiplying the reciprocal of that number?
Write in detail It's a fraction divided by a fraction

2/3÷4/5＝﹙2÷3﹚÷﹙4÷5﹚＝﹙2÷3﹚÷4×5＝﹙2÷3﹚×5÷4＝﹙2÷3﹚×﹙5÷4﹚＝2/3×5/4
This should be clear

Find the special solution of the differential equation (x-1) y '= y (1 + 2XY) satisfying the initial condition y (0) = 1

Y (x) = - 1 / (1 + x), after a while, it should be right

Plato, the ancient Greek philosopher, once pointed out that if M is an integer greater than 1, a = 2m, B = M2-1, C = M2 + 1, then a, B and C are Pythagorean numbers. Do you think it is correct? If correct, please explain the reason and use this conclusion to draw some Pythagorean numbers

Correct. Reason: ∵ m is an integer greater than 1, ∵ a, B, C are all positive integers, and C is the largest edge, ∵ (2m) 2 + (M2-1) 2 = (M2 + 1) 2, ∵ A2 + B2 = C2, that is, a, B, C are Pythagorean numbers. When m = 2, we can get a group of Pythagorean numbers 3, 4, 5

Write two divisions according to the multiplication

(1) So the answer is: 245, 35, 8245, 8, 35; 1235, 45, 371235, 37, 45