(a) Show that the functions f(t) = t2t1 and g(t) = t3 are linearly dependent on...
Problem 10. Let f,g: [a,b] -R be Riemann integrable functions such that f(x) < g(x) for all x E [a,b]. Prove that g(x)
QUESTION 2 Given two periodic functions, f(t) and g(t) is defined by and f (t) = cos, -<t<t f(t)= f(t +26) g(t) = cos, 0<t<2n g(t) = g(t +21) Sketch the graph of the periodic functions f(t) and g(t) over the interval (-37,37). Sketch in separate graphs. (Please use any online graphing software not hand-drawn). Find the Fourier series of f(t) and g(t). (b) Then, briefly comment what do you observe from the graphs and the Fourier series expansion of...
Please show full solution and explanation Consider the following two functions h (t) and f (t). and (a) Plot h(t) and f(t). (b)Use the convolution integral to calculate the convolution g (t) of the function h (t) with f (t) and plot. So if t > 0 h(t) = 1 et if t > 0 Ji if 0 <t<T f(t) = 10 if otherwise
Please show work for 1a through c. Will rate thumbs up for all parts shown! Thank you! 1. Find the Fourier coefficients of the given functions. (a) f(c) = (cos x + sin x)?, -1 < x < T; f(x + 2) = f(x) (b) f(x) = x, -1 < x < T; f(x + 2) = f(x) (b) f(x) = x, -1 < x < T; f(x + 2) = f(x) (c) f(x) = - <x<0, "; f(x +...
A periodic signal f(t) is produced by periodically repeating the function alt) - S2t|t| for -1<t<1 g(t) = to otherwise over the time domain-00<t<0. Determine the Fourier series representation of f(t) in the following forms. A. f(t) = a, + acos(nw,t) + b sin(nw,t); na1 B. f(0) = { Chelmuese n -00
Recall: Given two functions f(t) and g(t), which are differentiable on an interval I, • If the Wronskian W(8,9)(to) #0 for some to E I, then f and g are linearly independent for all te I. • If f(t) and g(t) are linearly dependent on I, then W (8,9)(t) = 0 for allt € 1. Note: This does NOT say that "If W(8,9)(x) = 0, then f(x) and g(2) are linearly dependent. Problem 2 Determine if the following functions are...
Problem 2 Determine if the following functions are linearly independent or linearly dependent. If you believe that they are linearly dependent (i.e. W(5,9) (+) = 0, for all t in some interval) find a dependence relation. 1. f(t) = cost, g(t) = sint 2. f(t) = 61, g(t) = 64+2 3. f(t) = 9 cos 2t, g(t) = 2 cos? t - 2 sinat 4. f(t) = 2t>, g(t) = 14
4. Suppose G is a group of order n < 0. Show that if G contains a group element of order n, then G is cyclic.
Find the Laplace transform of f(0) = 1, for 0 <t<1 5, for 1<t<2. e-l for t > 2
Find the Fourier series of the following functions in the given intervals. f(x) = r +, - <x< g(t) = { inter) 0. -T<r <0, sin(x), 0<x< 1.