Limits and Continuity | Mathematics Centre

Limits and continuity

• Limits
• Limit by Heine - Animations
  • Finite limit at x=a : if for every sequence {x_n} with a limit at a, the sequence of {f(x_n)} has a limit at g
    
  • Infinite limit at x=a; Vertical asymptote, x=a :
    
  • Limits at infinity; Horizontal asymptotes, y=L, y=M :
    
• Limit by Cauchy - Animations
  • The limit exists if no matter how small ε around g is set, one can always find δ around x₀ so that all the values f(x) around x₀ fall within ε from g
    
  • The limit does not exist if for some ε around g, no matter how small δ around x₀ is set some of the values f(x) around x₀ do not fall within ε from g
    
• Exercises - limits (Centrum Matematyki PG)
• Function continuity (Centrum Matematyki PG)
• Exercises - function continuity (Centrum Matematyki PG)
• Vocabulary - limits and continuity (Centrum Matematyki PG)