Check out this topic in the following free, online textbooks:
Introduction to Limits
Short explanations: Math BFF
Longer, lecture style: Prof. Leonard
Advanced topic - epsilon/delta proofs: Math By Fives
Limits and Continuity
Short explanations: ProfRobBob Far From Standard Tutoring
Videos for Specific probelms
MathisPower4U's Calculus I Video Library (left column)
Online Tutorials (including exercises with solutions)
Problem Sets with solutions
Drill in determining when a piecewise defined function is continuous.
Drill on evaluating limits.
Drill in finding horizontal asymptotes.
Drill on finding vertical asymptotes.
eCalculus.org and UC Davis Math
limit of a function as x approaches a fixed constant
limit of a function as x approaches plus or minus infinity
limit of a function using the precise epsilon/delta definition of limit
continuity of a function of one variable
Free Worksheets (with solutions)
Free Quizzes (with solutions)
A quiz on evaluating limits using the limit theorems and graphs.