3.1.1E: Funciones de Potencia (Ejercicios)
- Page ID
- 116463
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)sección 3.1 EJERCICIO
Encuentre el comportamiento a largo plazo de cada función como\(x \to \infty\) y\(x \to -\infty\)
1. \(f(x)=x^{4}\)
2. \(f(x)=x^{6}\)
3. \(f(x)=x^{3}\)
4. \(f(x)=x^{5}\)
5. \(f(x)=-x^{2}\)
6. \(f(x)=-x^{4}\)
7. \(f(x)=-x^{7}\)
8. \(f(x)=-x^{9}\)
Encuentra el grado y coeficiente principal de cada polinomio
9. \(4x^{7}\)
10. \(5x^{6}\)
11. \(5-x^{2}\)
12. \(6+3x-4x^{3}\)
13. \(-2x^{4} - 3x^{2} + x-1\)
14. \(6x^{5} -2x^{4} + x^{2} + 3\)
15. \((2x+3)(x-4)(3x+1)\)
16. \((3x+1)(x+1)(4x+3)\)
Encuentre el comportamiento a largo plazo de cada función como\(x \to \infty\) y\(x \to -\infty\)
17. \(-2x^{4} - 3x^{2} + x-1\)
18. \(6x^{5} -2x^{4} + x^{2} + 3\)
19. \(3x^{2} + x-2\)
20. \(-2x^{3} + x^{2} -x+3\)
21. ¿Cuál es el número máximo de\(x\) -intercepciones y puntos de inflexión para un polinomio de grado 5?
22. ¿Cuál es el número máximo de\(x\) -intercepciones y puntos de inflexión para un polinomio de grado 8?
¿Cuál es el menor grado posible de la función polinómica que se muestra en cada gráfica?
23. 
24
.25. 
26. 
27. 
28. 
29. 
30. 
Encuentra las intercepciones verticales y horizontales de cada función.
31. \(f(t)=2(t-1)(t+2)(t-3)\)
32. \(f(x)=3(x+1)(x-4)(x+5)\)
33. \(g(n)=-2(3n-1)(2n+1)\)
34. \(k(u)=-3(4-n)(4n+3)\)
- Contestar
-
1. Como\(x \to \infty\),\(f(x) \to \infty\) As\(x \to -\infty\),\(f(x) \to \infty\)
3. Como\(x \to \infty\),\(f(x) \to \infty\) As\(x \to -\infty\),\(f(x) \to -\infty\)
5. Como\(x \to \infty\),\(f(x) \to -\infty\) As\(x \to -\infty\),\(f(x) \to -\infty\)
7. Como\(x \to \infty\),\(f(x) \to -\infty\) As\(x \to -\infty\),\(f(x) \to \infty\)
9. \(7^{\text{th}}\)Titulación, Coeficiente principal 4
11. \(2^{\text{nd}}\)Titulación, Coeficiente principal -1
13. \(4^{\text{th}}\)Titulación, Coeficiente principal -2
15. \(3^{\text{rd}}\)Titulación, Coeficiente principal 6
17. Como\(x \to \infty\),\(f(x) \to -\infty\) As\(x \to -\infty\),\(f(x) \to -\infty\)
19. Como\(x \to \infty\),\(f(x) \to \infty\) As\(x \to -\infty\),\(f(x) \to \infty\)
21. intercepciones: 5, puntos de inflexión: 4
23. 3
25. 5
27. 3
29. 5
31. Intercepciones horizontales (1, 0), (-2, 0), (3, 0) Intercepción vertical (0, 12)
33. Intercepciones horizontales (1/3, 0) (-1/2. 0) Intercepción vertical (0, 2)