Properties of the limits

Limits

Definition of limit :

In mathematics, the concept of limit is used to describe the tendency of a succession or a function. The idea is that in a succession or a function, when speaking of limit, we say that has one if it is possible to be approached a certain number as much (that is, the limit) as we want

The study of the limits of functions of several variables is much more complex that the ones of of one variable , because in this, it only has two ways to approach a point, by the right or the left; whereas in the case of several variables a infinity of ways exists to approach us a point, as it shows in the figure 1.

figure 1

theorems of limits:

Theorem of limit1:

If k is a constant and to any number , then:

Theorem of limit2 :

To any number "a":

Theorem of limit3:

If m and b are two constants then:

Theorem of limit4:

Theorem of limit5:

Theorem of limit6:

If "f "is a polynomial and "a" is a real number, then

Theorem of limit7:

If q is a rational function and to it belongs to the dominion of q, then:

Theorem of limit8:

Solved Ejercises :

Solve the following limits indicating the property or properties that are applied in each ste

According to the theorem of limit 1:

Lim 77=77

x---3

f(x)= 3x-7 = mx+b that's why we apply the theorem of limit 3:

Lim 3x+7 = 3(5)-7 = 15-7

x--5

Lim = 8

x---5

Indeterminations

there are several types of indeterminations, among them: [refers to the limit to infinite and 0 the limit to 0 (not to number 0)]

videos of limits