this is in differential
equation subject . Please show your solvework in proper handwriting
to easier me to understand your work. Thanks



this is in differential equation subject . Please show your solvework in proper handwriting to easier me to understand y...
Consider the function y = x2 for x E (-7,7) . a) Show that the Fourier series of this function is n cos(nz) . b) (i) Sketch the first three partial sums on (-π, π) (ii) Sketch the function to which the series converges to on R . c) Use your Fourier series to prove that 2and1)"+1T2 12 2 2 Tu . d) Find the complex form of the Fourier series of r2. . e) Use Parseval's theorem to prove...
Q1 Write the following function in terms of unit step functions. Hence, find its Laplace transform 10<tsI g(t) = le-3, +1 , 1<t 2 .22 Q2 Use Laplace transform to solve the following initial value problem: yty(o)-0 and y (0)-2 A function f(x) is periodic of period 2π and is defined by Q3 Sketch the graph of f(x) from x-2t to2 and prove that 2sinh π11 f(x)- Q4 Consider the function f(x)=2x, 0<x<1 Find the a Fourier cosine series b)...
Let f(x) be the 27-periodic function which is defined by f(x)-cos(x/4) for-π < x < 1. π. (a) Draw the graph of y f(x) over the interval-3π < x < 3π. Is f continuous on R? (b) Find the trigonometric Fourier Series (with L π) for f(x). Does the series converge absolutely or conditionally? Does it converge uniformly? Justify your answer. (c) Use your result to obtain explicit values for these three series: 16k2 1 16k2 1 (16k2 1)2 に1...
3.(2 points) Determine whether the given function is periodic. If so, find its funda- mental period. (a) f(x) = 24 (b) f(x) = sin(ſx) (c) f(x) = ln x + cos x (d) f(x) = cos(65 4.(3 points) Sketch the graph of the given function defined on an interval (-0, 0) if (a) f(x) = e" for x > 0 and f(x) is an even function. (b) f(x) = {x, 0 < x < 2 (b) [(*) = 10, x=2...
function is defined over (0,6) by
f(x)={14x00<xandx≤33<xandx<6.
We then extend it to an odd periodic function of period 12
and its graph is displayed below.
calculate b1,b2,b3,b4, Thanks so much
A function is defined over (0,6) by 0<x and x <3 f (x) = 3<x and x < 6 We then extend it to an odd periodic function of period 12 and its graph is displayed below. 1.5 1 у 0.5 -10 5 10. 15 -1 -1.5 The function may be...
A causal discrete-time LTI system is described by the equationwhere z is the input signal, and y the output signal y(n) = 1/3x(n) + 1/3x(n -1) + 1/3x(n - 2) (a) Sketch the impulse response of the system. (b) What is the dc gain of the system? (Find Hf(0).) (c) Sketch the output of the system when the input x(n) is the constant unity signal, x(n) = 1. (d) Sketch the output of the system when the input x(n) is the unit step signal, x(n)...
Make sure everything is explained please, i'll rate for sure
Let f(1) = 123, 051<1 1, 1<r <2 a) Consider the even periodic extension, of period T = 4, of f(x). Sketch 3 periods, on the interval -6 <x< 6, of this function. an = 23 cos плх dr + 2 5 nr COS dr 2 b) Which of the integrals below can be used to find the Fourier cosine coefficients of the even periodic extension? (i) ( (ii) ja...
please explain and do in matlab
Problem 3. Consider the function f(x) e cos(2r). (1) Sketch its graph over the interval [0, m) by the following commands: (2) Using h = 0.01 π/6 in [0, π]. The commands are: to compute the difference quotient for z And the difference quotient is: ( 6 (3) Using h-0.01 to approximate the second derivative by computing the difdifquo for in [0, π). The commands are: And the difdifquo is:
Problem 3. Consider the...
l etisalat 5:45 PM 슐 moodle.ud.ac.ae 11.1 and 11.2 Fourier Series Q1 Find the Fourier series of the given function f(x), which is assumed to have the period 2π. Show the details of your work. Sketch or graph the partial sums up to that including cos 5x and sin 5x Note: Plot the partial sum using MATLAB Hint: Make use of your knowledge of the line equation to find f) from the given graph. 2 Find the Fourier integral representation...
A function is defined over (0,6) by 0 <and I <3 f(1) = - { 3<; and <6 We then extend it to an odd periodic function of period 12 and its graph is displayed below. N y 1 0 -10 5 5 10 15 X The function may be approximated by the Fourier series f (t) = a0 + 1 (an cos (021 ) + bn sin ( 122 )), where L is the half-period of the function. Use...