Limit as x Approaches Infinity

Limit as x Approaches Infinity

By Marissa Inoc

​What is the meaning of limit x as approaches infinity?​

we say a function f has a limit at infinity , if there exists a real number L such that for all ε​ > 0 , there exists N>0 such that. |f(x) - L| <ε for all x>N.

​

​The behavior of the function as the independent variable increases or decreases without bound

1. The Limit as x Increases Without bound

   let f(x) be a function that is defined at every number in some interval (a ,+∞). The limit of f(x) as x increases without bound is L and written as

   lim f(x) = L lim 1/x²=0

   ₓ→+∞ ₓ →+ ∞

​2. The Limit as x Decreases Without Bound

Let f(x) be a function that defined at every number in some interval (-∞ ,a ). the limit of f(x) as x decreases without bound is L , written as

lim f(x) = L lim 1 / x² = 0

​x→−∞ x→−∞

​3. If n is any positive integer , then

lim 1/xⁿ​ =0 lim 1/xⁿ = 0

x→ +∞ x​→−∞

​

To apply the theorem , divide each term of the numerator and denominator by the variable of the highest power occurring in either the numerator or denominator.​