Let p : R→ R be a non-constant polynomial, that is, for every x in R, p(x) = α0 + α1x+ ... + anx, with an + 0. Prove that, if n is even then lim→∞ p(x) = +∞ and limx→-∞ p(x) = +∞ when an > 0, and lim→∞ p(x) = · 0, and limÃ→∞ p(x) = −∞ and lim¸→-∞ p(x) = when an < 0 and n is odd.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Question
Let p : R→ R be a non-constant polynomial, that is, for every x in R, p(x) = α0 + α1x+
...
+ anx, with an + 0. Prove that, if n is even then lim→∞ p(x) = +∞ and
limx→-∞ p(x) = +∞ when an > 0, and lim→∞ p(x) =
· 0, and limÃ→∞ p(x) = −∞ and lim¸→-∞ p(x) =
when an < 0 and n is odd.
Transcribed Image Text:Let p : R→ R be a non-constant polynomial, that is, for every x in R, p(x) = α0 + α1x+ ... + anx, with an + 0. Prove that, if n is even then lim→∞ p(x) = +∞ and limx→-∞ p(x) = +∞ when an > 0, and lim→∞ p(x) = · 0, and limÃ→∞ p(x) = −∞ and lim¸→-∞ p(x) = when an < 0 and n is odd.
Expert Solution
steps

Step by step

Solved in 2 steps

Blurred answer
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,