1. Find the Laplace transform of the given function: View Solution
   • \(f(t) = 2u_{2}(t)+3(t-5)u_5(t)-7(t-3)^4\,u_3(t)\)
   • \(f(t) = (t-1)u_2(t)-2(t-2)u_1(t) \)
2. Find the Laplace transform of the given function: View Solution
   • \(f(t)=\begin{cases} t^2, & 0 \leq t < 3 \\ 1, & t \geq 3 \end{cases} \)
   • \(f(t)=\begin{cases} 1, & 0 \leq t < 2 \\ t, & 2 \leq t < 5 \\ 0, & t \geq 5 \end{cases} \)
3. Find the Laplace transform of given function: View Solution
   • \(f(t) = 2u(t-1)(t-1)^2+3\delta(t-5) \)
   • \(f(t) = 2u(t-1) t^2+5\delta(t-3) \)
4. Find the Laplace transform of the following functions: View Solution
   • \(h(t) = e^{2t} * \sin (3t) \)
   • \(\displaystyle{h(t) = \int_0^t \cos (2v) \, dv }\)
   • \(\displaystyle{h(t) = \int_0^t e^{t-\tau} \cosh (\tau) \, d\tau }\)