Ejercicios de repaso sección 4.1

Evaluar las transformadas de Laplace.

  1. f(t)=2t4\hspace{0.5cm} f(t)=\mathrm{2}t^4
  2. f(t)=t2+6t3\hspace{0.5cm} f(t)=t^2+6t-3
  3. f(t)=t2e9t+cosh5t\hspace{0.5cm} f(t)=t^2-e^{-9t}+cosh{5}t
  4. f(t)=(t+1)3\hspace{0.5cm} f(t)=(t+1)^3
  5. f(t)=(etet)2\hspace{0.5cm} f(t)=(e^t-e^{-t})^2
  6. f(t)=(1+e2t)2\hspace{0.5cm} f(t)=(1+e^{2t})^2
  7. f(t)=(2t1)3\hspace{0.5cm} f(t)=(2t-1)^3
  8. f(t)=2sen2tcos2t\hspace{0.5cm} f(t)=2sen2tcos{2}t
  9. f(t)=etcosht\hspace{0.5cm} f(t)=e^tcosh{t}
  10. f(t)=etsenht\hspace{0.5cm} f(t)=e^tsenht
  11. f(t)={1,0t<11,t1\hspace{0.5cm} f(t)=\left\{\begin{matrix}-1,&0\le t<1\\1,&t\geq1\\\end{matrix}\right.
  12. f(t)={0,0t<1t,t1\hspace{0.5cm} f(t)=\left\{\begin{matrix}0,&0\le t<1\\t,&t\geq1\\\end{matrix}\right.
  13. f(t)={0,0t<12t2,t1\hspace{0.5cm} f(t)=\left\{\begin{matrix}0,&0\le t<1\\2t-2,&t\geq1\\\end{matrix}\right.
  14. f(t)={sent,0t<π0,tπ\hspace{0.5cm} f(t)=\left\{\begin{matrix}sent,&0\le t<\pi\\0,&t\geq\pi\\\end{matrix}\right.
  15. f(t)={2t+1,0t<10,t1\hspace{0.5cm} f(t)=\left\{\begin{matrix}2t+1,&0\le t<1\\0,&t\geq1\\\end{matrix}\right.