Ejercicios de repaso sección 3.2

Verificar si el conjunto de funciones es LI o LD en el intervalo dado.

  1. f1(x)=x    ∧    f2(x)=xln⁡∣x∣\hspace{0.5cm}f_1(x)=x \;\;\wedge\;\;f_2(x)=x\ln \left| x\right|

(0,∞)\hspace{0.3cm}(0, \infty)

  1. f1(x)=x12    ∧    f2(x)=x2\hspace{0.5cm}f_1(x)=x^{\frac{1}{2}} \;\;\wedge\;\;f_2(x)=x^2

(−∞,∞)\hspace{0.3cm}(-\infty, \infty)

  1. f1(x)=cos3x    ∧    f2(x)=sen3x\hspace{0.5cm}f_1(x)=cos3x \;\;\wedge\;\;f_2(x)=sen3x

(−∞,∞)\hspace{0.3cm}(-\infty, \infty)

  1. f1(x)=x2    ∧    f2(x)=x2ln⁡∣x∣\hspace{0.5cm}f_1(x)=x^{2} \;\;\wedge\;\;f_2(x)=x^{2}\ln \left| x\right|

(0,∞)\hspace{0.3cm}(0, \infty)

  1. f1(x)=0,    f2(x)=x    ∧    f3(x)=ex\hspace{0.5cm}f_1(x)=0,\;\; f_2(x)=x\;\;\wedge\;\; f_3(x)=e^{x}

(−∞,∞)\hspace{0.3cm}(-\infty, \infty)

  1. f1(x)=5,    f2(x)=cos2x    ∧    f3(x)=sen2x\hspace{0.5cm}f_1(x)=5,\;\; f_2(x)=cos^2x\;\;\wedge\;\; f_3(x)=sen^2x

(−∞,∞)\hspace{0.3cm}(-\infty, \infty)

  1. f1(x)=cos2x,    f2(x)=1    ∧    f3(x)=cos2x\hspace{0.5cm}f_1(x)=cos2x,\;\; f_2(x)=1\;\;\wedge\;\; f_3(x)=cos^2x

(−∞,∞)\hspace{0.3cm}(-\infty, \infty)

  1. f1(x)=x,    f2(x)=x−1    ∧    f3(x)=x+3\hspace{0.5cm}f_1(x)=x,\;\; f_2(x)=x-1\;\;\wedge\;\; f_3(x)=x+3

(−∞,∞)\hspace{0.3cm}(-\infty, \infty)

  1. f1(x)=ex,    f2(x)=e−2x    ∧    f3(x)=xe−2x\hspace{0.5cm}f_1(x)=e^x,\;\; f_2(x)=e^{-2x}\;\;\wedge\;\; f_3(x)=xe^{-2x}

(−∞,∞)\hspace{0.3cm}(-\infty, \infty)

  1. f1(x)=ex,    f2(x)=e−xcos2x    ∧    f3(x)=e−xsen2x\hspace{0.5cm}f_1(x)=e^x,\;\; f_2(x)=e^{-x}cos2x\;\;\wedge\;\; f_3(x)=e^{-x}sen2x

(−∞,∞)\hspace{0.3cm}(-\infty, \infty)