Let be a function defined by:
We define by extension the odd, periodic function of period p = 2
which coincides with the function f (x) on the interval [0, 1].
Draw over the interval [−1, 3] the graph of the function towards
which the Fourier series of the odd continuation of the function f
(x) converges.
Homework Answers
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Let be a function defined by:
We define by extension the odd, periodic function of period...
We consider a periodic function of period p = 4 defined by: Draw the graph of...
We consider a periodic function of period p = 4 defined by:
Draw the graph of the function to which the Fourier series of the
function g (x) converges on the interval [−6, 6]
x + 2, g(x) -2 < x < 0; 0 < x < 2. 1- x,
We consider an even and periodic function of period p = 6 defined by: Calculate f...
We consider an even and periodic function of period p = 6
defined by:
Calculate f (17.75). Justify your answer.
f(x) = 2 + e-*, pour 0 < x < 3.
Sketch the function with its (a) odd periodic extension and (b) even then find the Fourier...
Sketch the function with its (a) odd periodic extension and (b) even then find the Fourier Sine and Fourier Cosine series, respectively. periodic extension, 0< x < X f(x) = -< x< 2 2
Sketch the function with its (a) odd periodic extension and (b) even then find the Fourier Sine and Fourier Cosine series, respectively. periodic extension, 0
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...
A periodic function ft) of period T-2 is defined as ft)-2t over the period (a) Sketch...
A periodic function ft) of period T-2 is defined as ft)-2t over the period (a) Sketch the function over the interval -3m<<3x. [3] (b) Find the cireular frequency a and the symmetry of the function (odd, even or neither). 21 (e) Determine the trigonometric Fourier coefficients for the function f) [10] (d) Write down its Fourier series for n=0, 1, 2, 3 where n is the harmonic number. [5] (e) Determine the Fourier series for the function g(t)-2r-1 over the...
3. Consider the periodic function defined by -ae sin(x) 0 x < 7T f(x) and f(x)...
3. Consider the periodic function defined by -ae sin(x) 0 x < 7T f(x) and f(x) f(x2t) - (a) Sketch f(x) on the interval -37 < x < 3T. (b) Find the complex Fourier series of f(x) and obtain from it the regular Fourier series
We define a function by: and we suppose that f (x + 2) = f (x)...
We define a function by:
and we suppose that f (x + 2) = f (x) for all x ∈ R.
(a) Draw the graph of the function f (x) over the interval [−3,
3].
(b) Find the Fourier series for the function f (x).
f(x) = { x +1 si -1 < x < 0; si 0 < x <1, 1
Calculate the even extension, the odd extension and the periodic extension (all three sets of coefficients)...
Calculate the even extension, the odd extension and the periodic
extension (all three sets of coefficients) Fourier series for the
functions:
1. f(x)=0 for 0<x<1/2 and f(x)=2 for 1/2<x<1, so
L=1;
2. f(x)=x on [0,1]
3. f(x)=Cos(3x) on [0,Pi]
Calculate the even extension, the odd extension and the periodic extension (all three sets of coefficients) Fourier series for the functions: 1. f(x)=0 for 0<x<1/2 and f(x)=2 for 1/2<x<1, so L=1; 2. f(x)=x on [0,1] 3. f(x)=Cos(3x) on [0,Pi]
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...
5. (a) (6) Carefully sketch the odd periodic extension, of period 2m, of the function f(x)1, 0 < x < π. (Only sketch over the interval z E [-2π, 2π). (b) (10) Find the Fourier sine series o...
5. (a) (6) Carefully sketch the odd periodic extension, of period 2m, of the function f(x)1, 0 < x < π. (Only sketch over the interval z E [-2π, 2π). (b) (10) Find the Fourier sine series of the function in part (a)
5. (a) (6) Carefully sketch the odd periodic extension, of period 2m, of the function f(x)1, 0
We consider a periodic function of period p = 4 defined by:
Draw the graph of the function to which the Fourier series of the
function g (x) converges on the interval [−6, 6]
x + 2, g(x) -2 < x < 0; 0 < x < 2. 1- x,
We consider an even and periodic function of period p = 6
defined by:
Calculate f (17.75). Justify your answer.
f(x) = 2 + e-*, pour 0 < x < 3.
Sketch the function with its (a) odd periodic extension and (b) even then find the Fourier Sine and Fourier Cosine series, respectively. periodic extension, 0< x < X f(x) = -< x< 2 2
Sketch the function with its (a) odd periodic extension and (b) even then find the Fourier Sine and Fourier Cosine series, respectively. periodic extension, 0
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 periodic function ft) of period T-2 is defined as ft)-2t over the period (a) Sketch the function over the interval -3m<<3x. [3] (b) Find the cireular frequency a and the symmetry of the function (odd, even or neither). 21 (e) Determine the trigonometric Fourier coefficients for the function f) [10] (d) Write down its Fourier series for n=0, 1, 2, 3 where n is the harmonic number. [5] (e) Determine the Fourier series for the function g(t)-2r-1 over the...
3. Consider the periodic function defined by -ae sin(x) 0 x < 7T f(x) and f(x) f(x2t) - (a) Sketch f(x) on the interval -37 < x < 3T. (b) Find the complex Fourier series of f(x) and obtain from it the regular Fourier series
We define a function by:
and we suppose that f (x + 2) = f (x) for all x ∈ R.
(a) Draw the graph of the function f (x) over the interval [−3,
3].
(b) Find the Fourier series for the function f (x).
f(x) = { x +1 si -1 < x < 0; si 0 < x <1, 1
Calculate the even extension, the odd extension and the periodic
extension (all three sets of coefficients) Fourier series for the
functions:
1. f(x)=0 for 0<x<1/2 and f(x)=2 for 1/2<x<1, so
L=1;
2. f(x)=x on [0,1]
3. f(x)=Cos(3x) on [0,Pi]
Calculate the even extension, the odd extension and the periodic extension (all three sets of coefficients) Fourier series for the functions: 1. f(x)=0 for 0<x<1/2 and f(x)=2 for 1/2<x<1, so L=1; 2. f(x)=x on [0,1] 3. f(x)=Cos(3x) on [0,Pi]
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...
5. (a) (6) Carefully sketch the odd periodic extension, of period 2m, of the function f(x)1, 0 < x < π. (Only sketch over the interval z E [-2π, 2π). (b) (10) Find the Fourier sine series of the function in part (a)
5. (a) (6) Carefully sketch the odd periodic extension, of period 2m, of the function f(x)1, 0
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