1. (3 points each) Find the following functions, (a) L{(t – 1)-step(t – 4)}
1. (3 points each) Find the following functions, (a) L{(t – 1) step(t – 4)} -4.5 (b) £'{S-2} } 2s + 1 (C) L-'{ s2 + 6s + 25
1. (3 points each) Find the following functions, (a) _{(t - 1) step(t – 4)} (b) L-44 S- 2s +1 (c) C-{ 32 +63 + 25
Find the Laplace transform of each of the following functions. 1. $(t) = f*(4(t – 1)* sin(67) dt L{v(t)}(s) = b. g(t) = [ e 2-3(t-1) cos(71) dT L{$(t)}(s) = c. y(t) = e5(t-1) sin(97) cos(6(t – T)) dt L{s(t)}(s) =
2. (8 points) Find the Laplace transform of each of the following functions. 1. 2 (t) = + cos 3+ + 3e-24 2. 2 (t) = (1 - *) (Hint: expand...) 3. 2 (t) = tsin? t (Hint: use half angle formula first...) 4. 2 (t) = cos(36) - 1
2. (8 points) Find the Laplace transform of each of the following functions. 1. 2 f(t) = 14 + cos 3t + 3e-2t 2. 2 h(t) = (1 - 3t)? (Hint: expand...) 3. 2 g(t) = t sin’t (Hint: use half angle formula first...) 4. 2 h(t) = e-2 cos(v3t) - tet
Express f in terms of unit step functions. fo) 1- 3 t-(t-1)2(t-1)-T(t-4) O t2(t-4) O t-1+ (t-4) O ti(t-1) _ (t-1)- (t-4) Find f(t) and Xset f(t). (Enter your answer in terms of s.) Xiet f(t))
Problem 1. (15 points each) For the signal f (t) f(t) 3 2 せ - 1 2 3 a) Describe signal f (t) in a compact form by using unit step functions b) Find and sketch(t) dt
Consider the following functions: f(x) = V8 - 4 and g(x) Step 1 of 3: Find four ordered pairs that satisfy the function, f(x) = =4 Answer ). D]
Express the following functions in terms of unit step functions and find the Laplace transforms. 2 f(t)= 0 0<ts 1<t<21 t> 21 sint (12 marks)
3. (8 points, 4 points each) f(x)-2x - 1 and g(x)-3x + 4, are functions from R to R. Find a. fog b. gof