Next Topic - Infinite Limits & Limits at Infinity

#Study Notes on Limits in Mathematics

#Table of Contents

Introduction to Limits
One-sided Limits
Two-sided Limits
Nonexistent Limits
Practice Questions
Glossary
Summary and Key Takeaways
Exam Strategies

#Introduction to Limits

#What are Limits in Mathematics?

Limits help us understand the behavior of functions as their input values approach a certain point. They are fundamental to calculus and are used to define derivatives and integrals.

Key Concept

Understanding limits is crucial because they form the foundation for many concepts in calculus.

#Key Points:

Limits describe the value that a function approaches as the input approaches a certain point.
Notation: $\lim_{{x \to c}} f(x)$ indicates the limit of the function $f(x)$ as $x$ approaches $c$ .
If the limit exists, $\lim_{{x \to c}} f(x) = R$ , where $R$ is a real number.

**Example**: For the function

f(x) = \frac{1}{x}

, as

x

approaches 0, the function becomes unbounded. Hence,

\lim\_{{x \to 0}} \frac{1}{x}

does not exist.

Exam Tip

Exam Tip: Always check the behavior of the function from both sides of the point in question.

#One-sided Limits

#What are One-sided Limits?

One-sided limits focus on the value of a function as the input approaches a certain point from one side only...