Question 6 (4 points) Determine which of the following statements is true. The Laplace transform and its inverse require integration of a function with an exponent e the ODE O No correct answer The Laplace transform and its inverse require differentiation of a function with an exponent e of the ODE O The Laplace transform requires integration of a function with an exponent e Save -st which is the eigenvalue of -st which is the eigenvalue -st which is the eigenfunction of the ODE Question 7 (4 points) Which of the following statements about the Laplace transform is FALSE? O The Laplace transform is defined for t<0 O The Laplace transform is an integral transform f(t) = (L(f(t))); ie, the inverse Laplace transform of the Laplace transform of some function f(t) returns the original function f(t) O All answers are correct Save Question 8 (4 points) Assuming (f(t)) F(s), what is (af(t))? O F(as) OF(s+a) = No correct answer O aF(s) Save Question 9 (4 points) Which of the following is the correct mathematical definition of the Laplace transform of some function f(t)? O No correct answer O F(s) = £(f) = √ ef(t)dt O =L(f)= F(s) - £(f) - e- est f(t)dt OF(w)=L(f). = 1 √2πT -iwt f(t)dt Question 10 (4 points) Which of the following statements about the Laplace transform is FALSE? O The Laplace transform is an integral transform O The Laplace transform is linear; ie, L(af(t) + bg(t)) = aL(f(t)) + bL(g(t)) No correct answer The Laplace transform is defined only for t0