This page has been robot translated, sorry for typos if any. Original content here.

# Cheat Sheets and Formulas

n Click image to view full size n

## Abbreviated Multiplication Formulas

Amount square:
( a + b ) 2= a 2+ 2 ab + b 2

Difference squared:
( a - b ) 2= a 2- 2 ab + b 2

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

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

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

Sum of squares:
a 2+ b 2 - cannot be expanded

The 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 a 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 the difference of the limits:

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

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

Limit function in degree:

Root limit of function:

### Basic limits

The first remarkable limit:

The second remarkable limit:

Other useful limit formulas are:

### Infinitely small

Equivalence of infinitely small:

## Derivatives Table

### Basic rules for 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 product:

Derivative fraction:

The derivative of a complex function:

### Formulas for differentiation of some elementary functions

Power function:

Root:

Indicative and logarithmic functions:

Trigonometric functions:

Indicative-power function: