Limit laws for a function, f, of one independent variable, x

Let c be a constant and let the following limits exist:

lim f(x) lim g(x)

x → a x → a

Then the following limit laws apply.

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

x → a x → a x → a

lim [ f(x) ˗ g(x) ] = lim f(x) ˗ lim g(x)

x → a x → a x → a

lim [ cf(x)] = c lim f(x)

x → a x → a

lim [ f(x) g(x) ] = lim f(x) ∙ lim g(x) (Product Rule)

x → a x → a x → a

lim [ f(x) / g(x) ] = lim f(x) / lim g(x) (Quotient Rule)

x → a x → a x → a

provided that lim g(x) ≠ 0

x → a

lim [ f(x) ]ⁿ = [ lim f(x) ]ⁿ ( where n is a positive integer)

x → a x → a

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