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6) True or False? (justify your answers a) I f ft) is piece wise Continuous on...
MACT 2141 Problem 6. (5 pts each) True or False (Cirele one and state your reason a. If J(t) is a solution of the DE:'+( tA 2019 4y5, then so is the function Reason: True False f and g be two functions, such that F(s) Lf ()) and G(s) Lig()) are defined on (0, oo). If f(t) S g(t) for all t 2 0, then F(s) S G(s) for all s >0. True False Reason: c. There exists a piecewise...
c. There exists a piecewise continuous and exponential order function that L[f(t)] = 3. True False Reason c. There exists a piecewise continuous and exponential order function that L[f(t)] = 3. True False Reason
6. (5 pts each) True or False (Cirele one and state your em) reason) a IE f(e) is a solution of the DE: y+(i ty + 4y 5, then so is the uo sit)--f(t) Reason: True b. Let f and g be two functions, such that F(s) Lif(t) and G(s)ig defined on (0, oo). If f(t) s g(t) for all t 20, then F(o) s G(o) for alls True Fais Reason: c. There exists a piecewise continuous and exponential order...
Show your complete work. 10 points. The Laplace transform of the piece wise continuous o<t<3 is given by: a) None of them 6) L {f} = = (2-e-st), S70 c)L{f} = 2 (3-e-st), s so dX[f) = 4 (1-2 est), so e) L {f} = } Show your complete wone. = ₃ (1-3e-st), 530
Consider the following statements. (i) Spring/mass systems and Series Circuit systems we covered are examples of linear dynamical systems in which each mathematical model is a second-order constant coefficient ODE along with initial conditions at a specific time. (ii) The following is an example of a piece-wise continuous function f (x) = { x x ∈ Q 0 x ∈ R \ Q (iii) It is unclear whether series solutions to ODEs even exist, and knowing about series solutions to...
Problem #1: Consider the following statements, [6 marks) 6) There is a systematic way of computing solutions to homogeneous second-order linear constant coefficient ODES. (ii) It is necessary for a function to be of exponential order in order for its Laplace Transform to be defined for some values of s. (iii) It is unclear whether series solutions to ODEs even exist, and knowing about series solutions to ODEs is mostly irrelevant in applications. (iv) There is only one way to...
g is [0,infinity) Question 6 (15 points) Let be a piecewise continuous function of exponential order on [ ) 0, oo . Use the Laplace transform to solve the following initial value problem d2y dt2
23 43 Problem 6. (5 pts each) True or False (Circle one and state your seaon) If t) is a solution of the DE: "+(t-t)y+Ay- 5, then so is the f Reason: rue Fa b. Let f and g be two functions, such that F(s)L0) and Go)-Li defined on (0, oo). If f(t) S 9(t) for allt 2 0, then F(o) S Glo) for als True F Reason: c. There exists a piecewise continuous and ex that LIf(0)]-3 exponential order...
For full credit, you must show all work and box answers 1. If functions f and g are piecewise continuous on the interval [0, oo), then the convolution of f and g is a function defined by the integral The Convolution Theorem (theorem 7.4.2 in your book and formula 6 in your table) states: If j(t) and g) are piecewise continuous on [0, oo) and of exponential order, then We are going to use convolution to solve y"-y,-t-e-,, y(0)-0, y'(0)-0....
8. [6 pts) Find a formula (possibly a piece-wise one) that defines a continuous function f on the interval |-1,2] such that I f(x) dx = " and " f(a) da = 2.