17-1: **Explain why a polynomial of degree 3 has at least one root.**Start by examining the end-behavior of a polynomial of degree 3. Which statement correctly describes the end-behavior of a polynomial of degree 3?- **A.** If $ f(x) $ has a leading term of $ ax^3 $, then either $\lim_{x \to \infty} f(x) = \infty$ and $\lim_{x \to -\infty} f(x) = -\infty$ when $ a > 0 $, or $\lim_{x \to \infty} f(x) = -\infty$ and $\lim_{x \to -\infty} f(x) = \infty$ when $ a < 0 $.- **B.** If $ f(x) $ has a leading term of $ ax^3 $, then either $\lim_{x \to \infty} f(x) = \infty$ and $\lim_{x \to \infty} f(x) = -\infty$ when $ a > 0 $, or $\lim_{x \to \infty} f(x) = -\infty$ and $\lim_{x \to \infty} f(x) = \infty$ when $ a < 0 $.- **C.** If $ f(x) $ has a leading term of $ ax^3 $, then $\lim_{x \to \infty} f(x) = \lim_{x \to -\infty} f(x) = b$ for some real number $ b $.

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Description: 17-1: **Explain why a polynomial of degree 3 has at least one root.**Start by examining the end-behavior of a polynomial of degree 3. Which statement correctly describes the end-behavior of a polynomial of degree 3?- **A.** If $ f(x) $ has a leadin

According to the given information, it is required to tell why a polynomial of degree 3 that has at…

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Explain why a polynomial of degree 3 has at least one root. Start by examining the end-behavior of a polynomial of degree 3. Which statement correctly describes the end-behavior of a polynomial of degree 3? OA If f(x) has a leading term of ax', then either lim f(x) = 00 and lim f(x) = 00 when a > 0 or lim f(x) = - ∞ and lim f(x) = - ∞ when a <0. x-- 00 x-00 x-- 0 O B. If f(x) has a leading term of ax", then either lim f(x) = 0o and lim f(x) = - o when a >0 or lim f(x) = - ∞ and lim f(x) = o∞0 when a <0. X- 00 X00 X- 00 Oc. If f(x) has a leading term of ax°, then lim f(x) = lim f(x) = b for some real number b. X- 00

Explain why a polynomial of degree 3 has at least one root. Start by examining the end-behavior of a polynomial of degree 3. Which statement correctly describes the end-behavior of a polynomial of degree 3? OA If f(x) has a leading term of ax', then either lim f(x) = 00 and lim f(x) = 00 when a > 0 or lim f(x) = - ∞ and lim f(x) = - ∞ when a <0. x-- 00 x-00 x-- 0 O B. If f(x) has a leading term of ax", then either lim f(x) = 0o and lim f(x) = - o when a >0 or lim f(x) = - ∞ and lim f(x) = o∞0 when a <0. X- 00 X00 X- 00 Oc. If f(x) has a leading term of ax°, then lim f(x) = lim f(x) = b for some real number b. X- 00

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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Concept explainers

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.

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Question

17-1:

**Explain why a polynomial of degree 3 has at least one root.**

Start by examining the end-behavior of a polynomial of degree 3. Which statement correctly describes the end-behavior of a polynomial of degree 3?

- **A.** If $ f(x) $ has a leading term of $ ax^3 $, then either $\lim_{x \to \infty} f(x) = \infty$ and $\lim_{x \to -\infty} f(x) = -\infty$ when $ a > 0 $, or $\lim_{x \to \infty} f(x) = -\infty$ and $\lim_{x \to -\infty} f(x) = \infty$ when $ a < 0 $.

- **B.** If $ f(x) $ has a leading term of $ ax^3 $, then either $\lim_{x \to \infty} f(x) = \infty$ and $\lim_{x \to \infty} f(x) = -\infty$ when $ a > 0 $, or $\lim_{x \to \infty} f(x) = -\infty$ and $\lim_{x \to \infty} f(x) = \infty$ when $ a < 0 $.

- **C.** If $ f(x) $ has a leading term of $ ax^3 $, then $\lim_{x \to \infty} f(x) = \lim_{x \to -\infty} f(x) = b$ for some real number $ b $.

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