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# Cribs and Formula

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## Formulas of abridged multiplication

Square of the sum:
( a + b ) 2= a 2+ 2 ab + b 2

The square of the difference:
( a - b ) 2= a 2- 2 ab + b 2

Cube amount:
( a + b ) 3= a 3+ 3 a 2b + 3 b 2a + b 3

Cube difference:
( a - b ) 3= a 3- 3 a 2b + 3 b 2a - b 3

The Binom-Newton formula:
( a + b ) n= C 0na n+ C 1na n - 1b + ... + C kna n - kb k+ C nnb n , the coefficients C kn= n ! / [ k ! ( n? k )!]

Sum of squares:
a 2+ b 2 - does not decompose

Difference of squares:
a 2- b 2= ( a - b ) ( a + b )

Sum of cubes:
a 3+ b 3= ( a + b ) ( a 2- ab + b 2)

Cube difference:
a 3- b 3= ( a - b ) ( a 2+ ab + b 2)

## Limits

### Basic rules for finding limits

The limit of constant value is equal to a constant value:

The limit of the sum is equal to the sum of the limits:

The difference limit is equal to the difference of limits:

The limit of the product is equal to the product of the limits:

The limit of the ratio is equal to the ratio of the limits:

Limit of function to degree:

Root limit of the function:

### Basic limits

First remarkable limit:

The second remarkable limit:

Other useful limit formulas are:

### Infinitely small

The equivalence of infinitesimals:

## The table of derivatives

### Basic rules of differentiation

Derivative constant:

The derivative of the sum is equal to the sum of the derivatives:

The derivative of the difference is equal to the difference of the derivatives:

Derivative of the work:

Derivative fraction:

Derivative of a complex function:

### Formulas for differentiation of certain elementary functions

Power function:

Root:

Exponential and logarithmic functions:

Trigonometric functions:

Exponential-power function: