Limits
Limits are a fundamental concept in calculus and are an essential tool for solving problems in various fields of mathematics, engineering, and science. A limit essentially describes the behavior of a function as the input (usually denoted as x) approaches a certain value. This value could be a specific number or even positive or negative infinity.
Limits are foundational in calculus because they allow us to define concepts like continuity, derivatives, and integrals. They're essential for understanding how functions behave at specific points and as they approach infinity or negative infinity.
IB Math deals with basics of limits. Basic of limits includes including the definition of limits, limit notation, types of limits and how to evaluate limits.
There are different ways to express limits mathematically. The most common notation used to represent the limit of a function is as follows:
In calculus a also limit can be determined from one side. One-sided limit refers to either x approaches from left or right side of value.
Limit from left side:
Limit from right side:
If both right side and left side limit equals to each other then limit exists.
Existence of a limit:
If 
then exists
There are three types of limits: finite limits, infinite limits, and limits at infinity.
A finite limit is a limit where the function approaches a finite value as the input value approaches a particular value. In other words, the limit exists and is a real number.
An infinite limit is a limit where the function approaches positive or negative infinity as the input value approaches a particular value. In other words, the limit does not exist, and the function value becomes infinitely large (or small) as the input value gets closer and closer to a particular value.
A limit at infinity is a limit where the input value approaches infinity or negative infinity, and the function approaches a finite value or infinity. In other words, the function value gets closer and closer to a particular value or infinity as the input value becomes infinitely large (or small).
There are different methods to evaluate limits, including direct substitution, factoring, rationalization, and L’Hopital’s Rule.
Direct substitution is a method used to evaluate limits by substituting the limit point into the function and simplifying the expression. This method works when the function is continuous at the limit point.
In some cases indeterminate form of limit occurs. Zero over Zero is one case for indeterminate form of limit. Zero over zero case can be solved by factoring, rationalizing, trigonometric identities, and L’Hopital’s Rule.
Graphical analysis is also one way to solve limits. This involves plotting the function and observing its behavior around the point in question.
In IB Math AA syllables Limit Concept seen at
IB Math SL AA Topic 5 Calculus – Limit
IB Math HL AA Topic 5 Calculus – Limit
There is no formula about Limits in IB Math Data booklet. But some trigonometric identities can be used for limits. (data bookleta link verebiliriz)
EduIB Questionbank gives you opportunity to solve real past paper like questions about Limits, Indeterminate Form, Limits at infinity.
For example one of Lmits in EduIB is shown below. It is very simi ar to IB Math SL Exam in November 2013.
