Homework Answers
function is defined over (0,6) by f(x)={14x00<xandx≤33<xandx<6. We then extend it to an odd periodic function of...
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...
0 3 and z s 6 We then extend it to an odd periodic function of period 12 and its graph is display...
0 3 and z s 6 We then extend it to an odd periodic function of period 12 and its graph is displayed below 2 y 1 -105 5 10 15 2 The function may be approximated by the Fourier series where L is the half-period of the function Use the fact that J(e) and fe)cL) are odd functions, enter the value of en in the box below f(z) cos an 0 for n 0,1,2,... Hence the Fourier series made...
A function is defined over (0,3) by f(3) = 12 +1. We then extend it to...
A function is defined over (0,3) by f(3) = 12 +1. We then extend it to an even periodic function of period 6 and its graph is displayed below. 2 15 0.5 5 10 15 х -0.5 The function may be approximated by the Fourier series f () = ap + 01 (an cos ( 122 ) + bn sin (022)). where L is the half-period of the function. Use the fact that f(x) sin is an odd functions, enter...
Given the periodic function 5 f(1) = { 1 f (+4) 0<i and I<2 2 <r...
Given the periodic function 5 f(1) = { 1 f (+4) 0<i and I<2 2 <r and I<4 otherwise and its graph is displayed below. 6 5 4 y 3 2 1 0 -2 2 4 6 00+ x The function may be approximated by the Fourier series f(t) = 40 + 1 (an cos ( 172 ) + bn sin where L is the half-period of the function. + bn sin ne :)), L Calculate the coefficients of the...
3. Consider the function defined by f(x) = 1, 0 < r< a, | 0, a<...
3. Consider the function defined by f(x) = 1, 0 < r< a, | 0, a< x < T, where 0a < T (a) Sketch the odd and even periodic extension of f (x) on the interval -3n < x < 3« for aT/2 (b) Find the half-range Fourier sine series expansion of f(x) for arbitrary a. (e) To what value does the half-range Fourier sine series expansion converge at r a? [8 marks
3. Consider the function defined by...
solve for L, A0, An, Bn, and f(x). (1 point) y= f(x) is the function illustrated...
solve for L, A0, An, Bn, and f(x).
(1 point) y= f(x) is the function illustrated below, defined only on в€ (0,6): Б 10 -1. -1 Compute the Fourier coefficients for f(x). Since we are only interested in the interval 0,6|, we don't care what happens anywhere else. We can pretend the function is zero on -6,0 and periodic: 10 57 19
(1 point) y= f(x) is the function illustrated below, defined only on в€ (0,6): Б 10 -1. -1...
Question 6 Consider the function defined over the interval 0<x<L. Extend f(x) as a function of...
Question 6 Consider the function defined over the interval 0<x<L. Extend f(x) as a function of period 2L by using an odd half-range expansion 1) Sketch the extended function over the interval -3L<XS3L. 2) Calculate the coefficients for the Fourier Series representation of the extended function. 3) Write the first 5 non-zero terms of the Fourier Series. (10 marks)
Consider the periodic function defined by 1<t0, 0<t<1, f(t)= f(t+2) f(), and its Fourier series F(t): Σ A,...
Consider the periodic function defined by 1<t0, 0<t<1, f(t)= f(t+2) f(), and its Fourier series F(t): Σ A, cos(nmi) +ΣB, sin (nπί), F(t)= Ao+ n1 n=1 (a) Sketch the function f(t) the function is even, odd or neither even nor odd. over the range -3<t< 3 and hence state whether (b) Calculate the constant term Ao
Consider the periodic function defined by 1
y=f(x)y=f(x) is the function illustrated below, defined only on x∈[0,6]x∈[0,6]: Complete the Fourier Coefficients? An is...
y=f(x)y=f(x) is the function
illustrated below, defined only on x∈[0,6]x∈[0,6]:
Complete the Fourier Coefficients? An is incorrect.
At least one of the answers above is NOT correct. 13 of the questions remain unanswered. (1 point) yf(z is the function illustrated below, defined only on E0,6 1.e 51 Compute the Fourier coefficlents for f(x) Now compute the cosine coefficients: An f)cos ()dz dr XCos(npix/6) -( d 0 Note: You can earn partial credit on this problem. Submit Answers Preview My Answers...
1. Consider the function defined by 1- x2, 0< |x| < 1, f(x) 0, and f(r) f(x+4) (a) Sketch the graph of f(x) on th...
1. Consider the function defined by 1- x2, 0< |x| < 1, f(x) 0, and f(r) f(x+4) (a) Sketch the graph of f(x) on the interval -6, 6] (b) Find the Fourier series representation of f(x). You must show how to evaluate any integrals that are needed 2. Consider the function 0 T/2, T/2, T/2 < T. f(x)= (a) Sketch the odd and even periodic extension of f(x) for -3r < x < 3m. (b) Find the Fourier cosine series...
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...
0 3 and z s 6 We then extend it to an odd periodic function of period 12 and its graph is displayed below 2 y 1 -105 5 10 15 2 The function may be approximated by the Fourier series where L is the half-period of the function Use the fact that J(e) and fe)cL) are odd functions, enter the value of en in the box below f(z) cos an 0 for n 0,1,2,... Hence the Fourier series made...
A function is defined over (0,3) by f(3) = 12 +1. We then extend it to an even periodic function of period 6 and its graph is displayed below. 2 15 0.5 5 10 15 х -0.5 The function may be approximated by the Fourier series f () = ap + 01 (an cos ( 122 ) + bn sin (022)). where L is the half-period of the function. Use the fact that f(x) sin is an odd functions, enter...
Given the periodic function 5 f(1) = { 1 f (+4) 0<i and I<2 2 <r and I<4 otherwise and its graph is displayed below. 6 5 4 y 3 2 1 0 -2 2 4 6 00+ x The function may be approximated by the Fourier series f(t) = 40 + 1 (an cos ( 172 ) + bn sin where L is the half-period of the function. + bn sin ne :)), L Calculate the coefficients of the...
3. Consider the function defined by f(x) = 1, 0 < r< a, | 0, a< x < T, where 0a < T (a) Sketch the odd and even periodic extension of f (x) on the interval -3n < x < 3« for aT/2 (b) Find the half-range Fourier sine series expansion of f(x) for arbitrary a. (e) To what value does the half-range Fourier sine series expansion converge at r a? [8 marks
3. Consider the function defined by...
solve for L, A0, An, Bn, and f(x).
(1 point) y= f(x) is the function illustrated below, defined only on в€ (0,6): Б 10 -1. -1 Compute the Fourier coefficients for f(x). Since we are only interested in the interval 0,6|, we don't care what happens anywhere else. We can pretend the function is zero on -6,0 and periodic: 10 57 19
(1 point) y= f(x) is the function illustrated below, defined only on в€ (0,6): Б 10 -1. -1...
Question 6 Consider the function defined over the interval 0<x<L. Extend f(x) as a function of period 2L by using an odd half-range expansion 1) Sketch the extended function over the interval -3L<XS3L. 2) Calculate the coefficients for the Fourier Series representation of the extended function. 3) Write the first 5 non-zero terms of the Fourier Series. (10 marks)
Consider the periodic function defined by 1<t0, 0<t<1, f(t)= f(t+2) f(), and its Fourier series F(t): Σ A, cos(nmi) +ΣB, sin (nπί), F(t)= Ao+ n1 n=1 (a) Sketch the function f(t) the function is even, odd or neither even nor odd. over the range -3<t< 3 and hence state whether (b) Calculate the constant term Ao
Consider the periodic function defined by 1
y=f(x)y=f(x) is the function
illustrated below, defined only on x∈[0,6]x∈[0,6]:
Complete the Fourier Coefficients? An is incorrect.
At least one of the answers above is NOT correct. 13 of the questions remain unanswered. (1 point) yf(z is the function illustrated below, defined only on E0,6 1.e 51 Compute the Fourier coefficlents for f(x) Now compute the cosine coefficients: An f)cos ()dz dr XCos(npix/6) -( d 0 Note: You can earn partial credit on this problem. Submit Answers Preview My Answers...
1. Consider the function defined by 1- x2, 0< |x| < 1, f(x) 0, and f(r) f(x+4) (a) Sketch the graph of f(x) on the interval -6, 6] (b) Find the Fourier series representation of f(x). You must show how to evaluate any integrals that are needed 2. Consider the function 0 T/2, T/2, T/2 < T. f(x)= (a) Sketch the odd and even periodic extension of f(x) for -3r < x < 3m. (b) Find the Fourier cosine series...
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