Maharashtra State BoardHSC Arts 11th

Concept of Limits


  • Definition of Limit
  • One-Sided Limit
  • Left-hand Limit
  • Right-hand Limit
  • Existence of a limit of a function at a point x = a
  • Algebra of limits:
    Let f(x) and g(x) be two functions such that
    `lim_(x→a) f(x) = l and lim_(x → a) g(x) = m, then`
    1. `lim_(x → a) [f(x) ± g(x)] = lim_(x → a) f(x) ± lim_(x → a) g(x) = l ± m`
    2. `lim_(x → a) [f(x) xx g(x)] = lim_(x→ a) f(x) xx lim_(x→ a) g(x) = l xx m`
    3. `lim_(x → a) [kf(x)] = k xx lim_(x→ a) f(x) = kl, "where" ‘k’ "is a constant"`
    4. `lim_(x → a) f(x)/g(x) = (lim_(x → a) f(x))/(lim_(x → a) g(x)) = l/m "where" m≠ 0`.
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