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7. Let a be a nonzero real number. Evaluate limr→ ∞ f(x) and limr+ -∞ f(x), where f (x) = ax – 3x* + 6x³ – 7x² + 10. State a result that guarantees the existence of a real root of the polynomial f(x) given the limits above. What would go wrong in this argument if we replace f(x) with a polynomial of an even degree?

7. Let a be a nonzero real number. Evaluate limr→ ∞ f(x) and limr+ -∞ f(x), where f (x) = ax – 3x* + 6x³ – 7x² + 10. State a result that guarantees the existence of a real root of the polynomial f(x) given the limits above. What would go wrong in this argument if we replace f(x) with a polynomial of an even degree?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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7. Let a be a nonzero real number. Evaluate lim- (x) and lim→ f(x), where -00 f (x) = ax – 3x* + 6x³ – 7x2 + 10. State a result that guarantees the existence of a real root of the polynomial f(x) given the limits above. What would go wrong in this argument if we replace f(x) with a polynomial of an even degree?
Transcribed Image Text:7. Let a be a nonzero real number. Evaluate lim- (x) and lim→ f(x), where -00 f (x) = ax – 3x* + 6x³ – 7x2 + 10. State a result that guarantees the existence of a real root of the polynomial f(x) given the limits above. What would go wrong in this argument if we replace f(x) with a polynomial of an even degree?
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