A monotonic bounded sequence must have a limit

Equivalent to infinitesimal

defined

Limit exists

The limit is equal to the function value at this point

Basic elementary functions are continuous within their domain

The first type of discontinuity point: both left and right limits exist

Type II discontinuities

All elementary functions are continuous within their definition interval

A continuous function on a closed interval must have a maximum and minimum value on the interval

A continuous function on a closed interval must be bounded on that interval

The function is continuous on the closed interval [a, b], and takes different function values ​​at the two endpoints of this interval, f(a)=A, f(b)=B, then for any number between A and B C, there is at least one point c in the open interval (a, b) such that f(c)=C (a<c<b)

second power

constant

Function with 0 as the limit

The sum and product of a finite number of infinitesimals are both infinitesimal

The product of a bounded function or constant and an infinitesimal is also infinitesimal

vertical asymptote

The reciprocal of infinity is infinitesimal

Left limit: x only approaches x0 from the left side of x0

Right limit: x only approaches x0 from the right side of x0

horizontal asymptote

If a sequence converges, then the sequence must be bounded

The limit of a convergent sequence is unique

The subsequences of a convergent sequence must converge

Area

Go to the realm of mind

Boundedness

Monotonicity

Parity

cyclical

If a function is defined on an interval and is monotonic on that interval, there must be an inverse function

inverse trigonometric function

Elementary function: a function composed of constants and basic elementary functions through a finite number of four arithmetic operations and a finite number of compound steps.

non-elementary functions