Let a be a nonzero real number. Evaluate lim, f(r) and lim, - f(z), where f(r) = ar" - 3r + 6z - 722 + 10. State a result that guarantees the existence of a real root of the polynomial f(r) given the limits above. What would go wrong in this argument if we replace f(x) with a polynomial of an even degree?

Let a be a nonzero real number. Evaluate lim, f(r) and lim, - f(z), where f(r) = ar" - 3r + 6z - 722 + 10. State a result that guarantees the existence of a real root of the polynomial f(r) 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

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Real analysis

Let a be a nonzero real number. Evaluate lim, x f(r) and lim, - f(r), where
f(x) = ar" - 3r* + 6z – 72 + 10.
State a result that guarantees the existence of a real root of the polynomial f(r) given the limits above.
What would go wrong in this argument if we replace f(r) with a polynomial of an even degree?

Branch of mathematical analysis that studies real numbers, sequences, and series of real numbers and real functions. The concepts of real analysis underpin calculus and its application to it. It also includes limits, convergence, continuity, and measure theory.

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