Write a function for which Laplace transformation doesnot exist. Explain why Laplace transform does not exist. 2. If L(f(t)) = F(s) what is L(e-atf(t))? 3. Find the Laplace transform of e-2t (1+t...

Write a function for which Laplace transformation doesnot exist. Explain why Laplace transform does not exist. 2. If L(f(t)) = F(s) what is L(e-atf(t))? 3. Find the Laplace transform of e-2t (1+t)2 . 4. Find the Laplace transform of te-t sint. 5. Find L(tsin2t). 6. state the condition for the existence of Laplace Transfrom of f(t). 7. Find the Laplace transform of t 1 . 8.Obtain the Laplace transform of sin2t-2tcos2t in the simplified form