Calculus 1000A/B Lecture 1: 1.3 One-Sided Limits

• School: Western University
• Department: Calculus
• Course: Calculus 1000A/B
• Professor: Rasul Shafikov

Document Summary

F (x) , then lim x a f (x) does not exist. If lim x a f (x) = l = lim x a f (x) , then lim x a f (x) = l . Note: lim x a f (x) = l means the left-hand limit of f (x) , as x approaches a is l or the limit of f(x) as x approaches a from below (from the left) is l . Consider the limit of f(x) as x approaches 1 of the following piece-wise defined function: Sketch the graph of f(x) f (x) = lim x 1 lim x 1 lim x 1. Therefore, lim x 1 f (x) = lim x 1 x 2 = 1. 3 x = 2 f (x) does not exist. A function f(x) is said to be continuous at a if lim x a f (x) = f (a)