end-behavior

end-behavior - n + a n-1 x n-1 + + a is a polynomial of...

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Lemma. For any real numbers a and b , | a + b | ≤ | a | + | b | . Proof. Proposition. Suppose f ( x ) = x n + a n - 1 x n - 1 + ··· + a 0 is a polynomial of degree n with leading coefficient 1. Let M be a positive real number. Suppose x > 1 + M + | a n - 1 | + ··· + | a 0 | . ( * ) Then f ( x ) > M . Proof. If ( * ) holds, then ... . Corollary. Suppose f ( x ) = a n x
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Unformatted text preview: n + a n-1 x n-1 + + a is a polynomial of degree n with leading coecient a n > 0. Let M be a positive real number. Then there is x such that: if x > x , then f ( x ) > M . Proof. 1...
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