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Limits at Infinity for Polynomials

# Limits at Infinity for Polynomials - Limits at Infinity for...

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Limits at Infinity for Polynomials

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To find the limit at infinity of a polynomial, take the limit of the term of the highest degree. ( 29 ( 29 x x lim x x lim x → ∞ → ∞ - + = 4 2 4 5 3 2 5
Now apply the Principles of Limits ( 29 ( 29 x x lim lim x → ∞ → ∞ = 4 5 = ⋅∞=∞ 5 ( 29 ( 29 x x lim x x lim x → ∞ → ∞ - + = 4 2 4 5 3 2 5

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Example for x approaching -∞ ( 29 ( 29 x x lim x x lim x - - - + = 4 2 4 5 3 2 5 ( 29 ( 29 x x lim lim x - - = 4 5 = ⋅∞=∞ 5
Example with negative leading coefficient ( 29 ( 29 x x lim x x lim x → ∞ → ∞ - - + = - 4 2 4 5 3 2 5 ( 29 ( 29 x x lim lim x → ∞ → ∞ = - 4 5 = - ⋅ ∞ = - ∞ 5

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( 29 ( 29 x x lim x x lim x - - - - + = - 4 2 4 5 3 2 5 ( 29 ( 29 x x lim lim x - - = - 4 5 = - ⋅ ∞ = - ∞ 5
These first examples have all had an even degree. The next 2 examples will have an

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