10. (a) 5pts] Prove that if f is piecewise continuous on [0,00) and satisfies the growth is, f(t) Me for restriction th...
The Laplace transform of the piecewise continuous function $4, 0<t<3 f(t) is given by 2, t> 3 1 L{f} (1 – 2e-st), 8 >0. S None of them L{f} = (1 – 3e®), s>0. 2 L{f} (3 - e-), 8 >0. S 2 L{f} (2-est), s >0. S
The Laplace transform of the piecewise continuous function $4, 0<t<3 f(t) is given by 2, t> 3 1 L{f} (1 – 2e-st), 8 >0. S None of them L{f} = (1 – 3e®), s>0. 2 L{f} (3 - e-), 8 >0. S 2 L{f} (2-est), s >0. S
Question 9 3 pts The Laplace transform of the piecewise continuous function 4, 0<t <3 f(t) is given by t> 3 (2, L{f} = { (1 – 3e-*), s>0. O 2 L{f} (2 - e-st), 8 >0. 2 L{f} = (3 - e-st), s >0. O None of them 1 L{f} (1 – 2e -st), s >0.
Question 9 3 pts The Laplace transform of the piecewise continuous function J4, 0< < 3 f(t) is given by 2, t> 3 2 L{f} (2 - e-st), 8 >0. S L{f} (1 – 3e-), 8>0. 8 2 L{f} (3 - e-s), 8 >0. S L{f} = (1 – 2e-st), s > 0. None of them Question 10 3 pts yll - 4y = 16 cos 2t To find the solution of the Initial-Value Problem y(0) = 0 the y...
1 Let f (t), g(t) be a continuous function on some interval I, and to e I. Prove that the initial value problem y'(t) f(t)y + g(t)y2, y(to) zo has a unique and continuous solution φ(t) on a small interval containing to, φ(t) satisfies the initial condition φ(to) = to. 1 Let f (t), g(t) be a continuous function on some interval I, and to e I. Prove that the initial value problem y'(t) f(t)y + g(t)y2, y(to) zo has...
a) i. Express in terms of the unit step function, the piecewise continuous causal functions (2t2, Ost<3 F(t) = {t + 4, 3 st<5 9, t25 [3 marks] ii. Use Laplace transforms to solve the initial value problem a) 7" + 16y = 4cos3t + s(t – 1/3) where y(0) = 0 and y'(0) = 0. [7 Marks) E.K. Donkoh (Ph.D) or [7 marks) B) y' – 3y = F(t), where y(0) = 0 and (sint, Osts F(t) = 1,...
Applied Mathematics Laplace Transforms 1. Consider a smooth function f(t) defined on 0 t<o, with Laplace transform F(s) (a) Prove the First Shift Theorem, which states that Lfeatf(t)) = F(s-a), where a is a constant. Use the First Shift Theorem to find the inverse trans- form of s2 -6s 12 6 marks (b) Prove the Second Shift Theorem, which states that L{f(t-a)H(t-a))-e-as F(s), where H is the Heaviside step function and a is a positive constant. Use the First and...
(10 marks) Prove that fx=6ln(x-11) is not uniformly continuous on (0,∞) Х Enable Editing X i PROTECTED VIEW Be careful—files from the Internet can contain viruses. Unless you need to edit, it's safer to stay in Protected View. LAAM Yuuuus = (x2-x-2 1. (10 marks) Let f(x) (x2-4) if x # +2 с if x = 2 Find c that would make f continuous at 1. For such c, prove that f is continuous at 1 using an ε -...
1. Determine whether the statement is true or false. If false, explain why and correct the statement (T/FIf)exists, then lim ()f) o( T / F ) If f is continuous, then lim f(x) = f(r) (TFo)-L, then lim f(x)- lim F(x) "( T / F ) If lim -f(x)s lim. f(x) L, then lim f(x)s 1. "(T/F) lim. In x -oo . (T/F) lim0 ·(T / F ) The derivative f' (a) is the instantaneous rate of change of y...
High pass digital filter The values of Resistor and Capacitor is shown as below R(2) 100000 C(F) 1.5432 10-6 e.1 (5pts) Please derive the Laplace transfrom equation V, (s) Vi(s) e.2(5pts) Please use bilinear transform equation to transform Laplace transform to 一? z-transform. Bilinear transform equation is shown as below: = T (1+2-1) Your result will be (2) =? Vi(z) e.3(10pts) Please use inverse z-transform to find the difference equation. Your result will be look like as below, you will...