basic calculus

• Theorem 1


  The limit of a constant is that constant
• Theorem 1


  Lim C = C
• Theorem 2


  Limit of the identity function
• Theorem 2


  Lim x = a

  x -> a
• Theorem 3


  The limit of a constant times a function is equal to the C times the limit of a function
• Theorem 3


  Lim C · f(x) = C Lim f(x)

  x -> a x -> a
• Theorem 4


  The limit of a sum f two functions is equal to the sum of the individual limit.
• Theorem 4


  Lim [f(x) + g(x)] = Lim f(x) + Lim g(x)

  x -> a x -> a x -> a
• Theorem 5


  The limit of the difference of the two functions is equal to the difference of the individual limit.
• Theorem 5


  Lim [f(x) - g(x)] = Lim f(x) - Lim g(x)

  x -> a x -> a x -> a
• Theorem 6


  The limit of the product of two functions is the product of their limit.
• Theorem 6


  Lim [f(x) · g(x)] = Lim f(x) · Lim g(x)

  x -> a x -> a x -> a
• Theorem 7


  The limit of the quotient of two functions is the quotient of their limits
• Theorem 7


  $Lim f(x)/g(x), x → a =$$Lim f(x), x → a/Lim g(x), x→ a$
• Theorem 8


  The limit of the nth power of a function is equal to the power of the limit of that function.
• Theorem 8


  Lim [f(x)]^n = [Lim f(x)]^n

  x → a x → a
• Theorem 9


  The limit of the nth root of a function is equal to the principal root of the limit of that function
• Theorem 9


  Lim n√f(x) = n√Lim f(x)

  x → a x → a