#Properties of Limits

#Table of Contents

1. Introduction to Limit Properties
2. Basic Limit Properties
   • Limit of a Constant Function
   • Limit of a Multiple of a Function
   • Limit of a Sum or Difference of Functions
   • Limit of a Product of Functions
   • Limit of a Quotient of Functions
   • Limit of the Power of a Function
   • Limit of a Composite Function
3. Infinite Limits
4. Practice Questions
5. Glossary
6. Summary and Key Takeaways

#Introduction to Limit Properties

Understanding limit properties (also known as limit theorems) is crucial for solving complex functions algebraically. These properties allow us to break down complicated functions into simpler parts, making it easier to determine their limits.

#Basic Limit Properties

#Limit of a Constant Function

If $k$ is a constant, then: $$\lim_{{x \to a}} k = k$$

#Limit of a Multiple of a Function

If $k$ is a constant and $\lim_{{x \to a}} f(x) = L$, then: $$\lim_{{x \to a}} (k f(x)) = kL$$

#Limit of a Sum or Difference of Functions

If $\lim_{{x \to a}} f(x) = L$ and $\lim_{{x \to a}} g(x) = M$, then: $$\lim_{{x \to a}} (f(x) \pm g(x)) = L \pm M$$

#Limit of a Product of Functions

If $\lim_{{x \to a}} f(x) = L$ and $\lim_{{x \to a}} g(x) = M$, then: $$\lim_{{x \to a}} (f(x) \cdot g(x)) = L \cdot M$$

#Limit of a Quotient of Functions

If $\lim_{{x \to a}} f(x) = L$ and $\lim_{{x \to a}} g(x) = M$ with $M \ne 0$, then: $$\lim_{{x \to a}} \frac{f(x)}{g(x)} = \frac{L}{M}$$

#Limit of the Power of a Function

If $\lim_{{x \to a}} f(x) = L$ and $n$ is a real number, then: $...