<> Basic formulas for derivation and differentiation :

<> McLaughlin formula :

<> Indefinite integral formula :

<> Approximate differential :

<> Three common cases of the second kind of transformation integral method :

<> Several formulas for finding higher derivative :

<> Permutation and combination formula :

C Calculation of :
The number of subscript numbers multiplied by the number of superscript numbers , And every number should be -1. Then divide the factorial of the above subject . as :C5 3( The subscript is 5, Superscript is 3)=(5X4X3)/3X2X1.
3X2X1( that is 3 factorial )
A Calculation of :
Follow C The first step is the same . Is the factorial without dividing by superscript .
as :A4 2 = 4X3 .

<> Induction formula :

Formula 1 :

set up α Is an arbitrary angle , The values of the same trigonometric function of the same angle with the same end edge are equal :

sin(2kπ+α)=sinα (k∈Z)

cos(2kπ+α)=cosα (k∈Z)

tan(2kπ+α)=tanα (k∈Z)

cot(2kπ+α)=cotα (k∈Z)

Formula 2 :

set up α Is an arbitrary angle ,π+α Trigonometric function value and α Relationship between trigonometric function values :

sin(π+α)=-sinα

cos(π+α)=-cosα

tan(π+α)=tanα

cot(π+α)=cotα

Formula 3 :

Arbitrary angle α And -α Relationship between trigonometric function values :

sin(-α)=-sinα

cos(-α)=cosα

tan(-α)=-tanα

cot(-α)=-cotα

Formula 4 :

Using formula 2 and formula 3, we can get π-α And α Relationship between trigonometric function values :

sin(π-α)=sinα

cos(π-α)=-cosα

tan(π-α)=-tanα

cot(π-α)=-cotα

Formula 5 :

Using formula 1 and formula 3, we can get 2π-α And α Relationship between trigonometric function values :

sin(2π-α)=-sinα

cos(2π-α)=cosα

tan(2π-α)=-tanα

cot(2π-α)=-cotα

Formula 6 :

π/2±α and 3π/2±α And α Relationship between trigonometric function values :

sin(π/2+α)=cosα

cos(π/2+α)=-sinα

tan(π/2+α)=-cotα

cot(π/2+α)=-tanα

sin(π/2-α)=cosα

cos(π/2-α)=sinα

tan(π/2-α)=cotα

cot(π/2-α)=tanα

sin(3π/2+α)=-cosα

cos(3π/2+α)=sinα

tan(3π/2+α)=-cotα

cot(3π/2+α)=-tanα

sin(3π/2-α)=-cosα

cos(3π/2-α)=-sinα

tan(3π/2-α)=cotα

cot(3π/2-α)=tanα

( above k∈Z)

<> Number set

Rational number , A general term for integers and fractions , All rational numbers can be converted into fractions .

real number , Rational number and irrational number .

Irrational number , Infinite acyclic number .

Natural number , All nonnegative integers .

Positive integers refer to 1,2,3,4,5…… That kind of number

Natural numbers include 0 Sum positive integer .

Integers include negative integers ,0, positive integer .

Integer means …… -3 -2 -1 0 1 2 3 …… That kind of number . Integers that are not natural numbers are negative integers , finger -1 -2 -3…… That kind of number .

A rational number is a number that can be written as the ratio of two integers . Rational numbers include integers and fractions , A fraction is a rational number that is not an integer , All finite and infinite cyclic decimals are fractions .

Real numbers are both rational numbers and irrational numbers . An irrational number is an infinite acyclic decimal , A real number that cannot be written as the ratio of two integers , All decimals and integers are real numbers .

real number ={ Rational number }∪{ Irrational number }

And the plural . Plural finger a+bi(a,b Is a real number , among i^2=-1) Number of forms . The plural number is a general term for real and imaginary numbers . among b=0 When, the complex number is a real number , Everything else is imaginary ,a=0,b≠0 Time is a pure imaginary number .

And super real numbers , Is the set of numbers that extends infinity and infinity decimals in the set of real numbers .

Natural number :N, positive integer :N+, integer :Z, Rational number :Q, real number :R, complex :C.

Natural number , positive integer , integer , Rational numbers are countable sets , Real and complex numbers are uncountable sets .

Countable sets are infinite sets that can correspond to natural numbers one by one , An uncountable set is an infinite set that cannot correspond to a natural set one by one . The number of digits of natural numbers is limited , The decimal part of a real number is infinite , So is the potential infinite or the real infinite exhausted , Real numbers are uncountable . Rational number , finish writing sth. p/q, List lattice , Diagonal arrangement can prove that rational numbers are countable .

A picture is worth a thousand words :

Real number set R It's continuous , This is also the basis of calculus .

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