5. Given a>0, let f(t) = 1 if 0St 0, let f(t) = 1 if 0St...

Transcribed Image Text:

5. Given a>0, let f(t) = 1 if 0St<a, f(t) = 0 iftz a. First, identify the correct sketch of the graph of the function f, making clear its value att= a. Then express f in terms of unit step functions to show that f0)} =s1(1-e " as). Remember that the unit step function is defined as follows. O for t<a 1 for tža u(t - a) =. " Cick the icon to view the table of Laplace transforms. Which is the correct sketch of the function? Choose the correct answer below. OA. B. OC. D. Ay Express f(t) in terms of the unit step function. A. f(t) =1+ u(t-a) B. f(t) =1- u(t - a) C. f(t) = u(t- a) +a D. f(1) = u(t- a) - 1 Show that f(t) = s(1-e-as). Choose the correct transformations and transform the expression at each step. K0) = (1). Apply the Laplace transform to both sides. = (2). (3) %3D (4) (List the terms in the same order as they appear in the original list. Type expressions using s as the variable.) =s (1-e-*) (5) 5. Given a>0, let f(t) = 1 if 0St<a, f(t) = 0 iftz a. First, identify the correct sketch of the graph of the function f, making clear its value att= a. Then express f in terms of unit step functions to show that f0)} =s1(1-e " as). Remember that the unit step function is defined as follows. O for t<a 1 for tža u(t - a) =. " Cick the icon to view the table of Laplace transforms. Which is the correct sketch of the function? Choose the correct answer below. OA. B. OC. D. Ay Express f(t) in terms of the unit step function. A. f(t) =1+ u(t-a) B. f(t) =1- u(t - a) C. f(t) = u(t- a) +a D. f(1) = u(t- a) - 1 Show that f(t) = s(1-e-as). Choose the correct transformations and transform the expression at each step. K0) = (1). Apply the Laplace transform to both sides. = (2). (3) %3D (4) (List the terms in the same order as they appear in the original list. Type expressions using s as the variable.) =s (1-e-*) (5)