Guide to Limits in Calculus
Comprehensive guide to Limits in Calculus, designed for students in the MCV4U course.
1. Introduction to Limits
A limit describes the value that a function f(x) approaches as the input x approaches a particular value. Limits are crucial for understanding continuity, derivatives, and integrals in calculus.
Notation:
\[ \lim_{x \to c} f(x) = L \]
This means as \(x\) approaches \(c\), \(f(x)\) approaches \(L\).
2. Types of Limits
a) Finite Limits at Finite Points
If \(f(x)\) approaches a specific value \(L\) as \(x \to c\), the limit exists.
Example:
\[ \lim_{x \to 2} (3x + 1) = 7 \]
Solution: Substitute \(x = 2\): \[ f(2) = 3(2) + 1 = 7 \]
\[ \lim_{x \to 2} (3x + 1) = 7 \]
Solution: Substitute \(x = 2\): \[ f(2) = 3(2) + 1 = 7 \]