Let f(x)={0−(4−x)for 0≤x<2,for 2≤x≤4. ∙ Compute the Fouriercosine coefficients for f(x).a0=an=What are...
Let f(x)={0−(4−x)for 0≤x<2,for 2≤x≤4. ∙ Compute the Fourier cosine coefficients for f(x).
a0=
an=
What are the values for the Fourier cosine series a02 + ∑n = 1∞ancos(nπ4x) at the given points.
x=2:
x=−3:
x=5:
Homework Answers
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Let f(x)={0−(4−x)for 0≤x<2,for 2≤x≤4. ∙ Compute the Fouriercosine coefficients for f(x).a0=an=What are...
Compute the Fourier cosine coefficients for f(x)
Let \(f(x)= \begin{cases}0 & \text { for } 0 \leq x<2 \\ -(4-x) & \text { for } 2 \leq x \leq 4\end{cases}\)- Compute the Fourier cosine coefficients for \(f(x)\).- \(a_{0}=\)- \(a_{n}=\)- What are the values for the Fourier cosine series \(\frac{a_{0}}{2}+\sum_{n=1}^{\infty} a_{n} \cos \left(\frac{n \pi}{4} x\right)\) at the given points.- \(x=2:\)- \(x=-3\) :- \(x=5:\)
4. Consider the following partial information about a function f(x): S.x2, 0<x<I, (2-x), 1<x<2. Given that...
4. Consider the following partial information about a function f(x): S.x2, 0<x<I, (2-x), 1<x<2. Given that the function can be extended and modelled as a Fourier cosine-series: (a) Sketch this extended function in the interval that satisfies: x <4 (b) State the minimum period of this extended function. (C) The general Fourier series is defined as follows: [1 marks] [1 marks] F(x) = 4 + ] Ancos ("E") + ] B, sin("E") [1 marks] State the value of L. (d)...
4. Let f(x) = 6-2x, 0
4. Let f(x) = 6-2x, 0<x 2 (a) Expand f(x) into a periodic function of period 2, ie. construct the function F(x), such that F(x)-f (x), 0xS 2, and Fx) F(x+2) for all real numbers x. (This process is called the "full-range expansion" of f(x) into a Fourier series.) Find the Fourier series of Fr). Then sketch 3 periods of Fx). (b) Expand fx) into a cosine series of period 4. Find the Fourier series and sketch 3 periods (c)...
FIND A0, An, Bn, and f(x) f(x) is the function illustrated below, defined only on x...
FIND A0, An, Bn, and f(x)
f(x) is the function illustrated below, defined only on x E [0,4]: y 4 110 -1 -1 Compute the Fourier coefficients for f(x). For this question, we will reflect the graph around the y-axis to get an even function: 1 0 -5 13 -1 We get L =4 (x)dx A0 =
f(x) is the function illustrated below, defined only on x E [0,4]: y 4 110 -1 -1 Compute the Fourier coefficients for f(x)....
Let f(x) = x.a) Expand f(x) in a Fourier cosine series for 0 ≤ x ≤...
Let f(x) = x.a) Expand f(x) in a Fourier cosine series for 0 ≤ x ≤ π.b) Expand f{x) in a Fourier sine series for 0 ≤ x < π.c) Expand fix) in a Fourier cosine series for 0 ≤ x ≤ 1.d) Expand fix) in a Fourier sine series for 0 ≤ x < 1.
Type or paste question here 3. (20 pts.) Consider the function f defined on (0, 2)...
Type or paste question here
3. (20 pts.) Consider the function f defined on (0, 2) by 2+1 f(x) = = { 0<x< 1 1<x< 2 (a) Denote by fs the sum of the sine Fourier series of f (on (0,2]). Plot the graph of the function fs for x € (-2, 4), indicating the values at each point in that interval. Compute fs(0) and fs(2). [You do not have to compute the coefficients of the Fourier series.] (b) Denote...
4. (35 pts) Let f(x) = x(1-x) for 0 < x < 1. (a) (15 pts) Compute the Fourier cosine series FCS f...
which part b uses the answer from part a.
4. (35 pts) Let f(x) = x(1-x) for 0 < x < 1. (a) (15 pts) Compute the Fourier cosine series FCS f(x). (b) (5 pta) Find the formal solution of the problem BC u,(O, t)-u(1,t)-0, (c) (5 pts) Show that there can be no solution of problem (A) which is Ca for 0 S S 1 and (d) (10 pts) Show that there is a Co solution of the DE...
2. Let f(x) = 8 + 3x4 -1 5x<1, f(x+2) = f(x). Which best describes the...
2. Let f(x) = 8 + 3x4 -1 5x<1, f(x+2) = f(x). Which best describes the Fourier series of f: (a) It is a Fourier cosine series. (b) It is a Fourier sine series. (c) It is a general Fourier series with sine and cosine terms.
solve for L, A0, An, Bn, and f(x). f(x) is the periodic function illustrated below: y...
solve for L, A0, An, Bn, and f(x).
f(x) is the periodic function illustrated below: y 1/0 -9 Compute the Fourier coefficients for f(x)
f(x) is the periodic function illustrated below: y 1/0 -9 Compute the Fourier coefficients for f(x)
3. Let f(x) = 1 – X, [0, 1] (a) Find the Fourier sine series of...
3. Let f(x) = 1 – X, [0, 1] (a) Find the Fourier sine series of f. (b) Find the Fourier cosine series of f. (Trench: Sec 11.3, 12) (Trench: Sec 11.3, 2)
4. Consider the following partial information about a function f(x): S.x2, 0<x<I, (2-x), 1<x<2. Given that the function can be extended and modelled as a Fourier cosine-series: (a) Sketch this extended function in the interval that satisfies: x <4 (b) State the minimum period of this extended function. (C) The general Fourier series is defined as follows: [1 marks] [1 marks] F(x) = 4 + ] Ancos ("E") + ] B, sin("E") [1 marks] State the value of L. (d)...
4. Let f(x) = 6-2x, 0<x 2 (a) Expand f(x) into a periodic function of period 2, ie. construct the function F(x), such that F(x)-f (x), 0xS 2, and Fx) F(x+2) for all real numbers x. (This process is called the "full-range expansion" of f(x) into a Fourier series.) Find the Fourier series of Fr). Then sketch 3 periods of Fx). (b) Expand fx) into a cosine series of period 4. Find the Fourier series and sketch 3 periods (c)...
FIND A0, An, Bn, and f(x)
f(x) is the function illustrated below, defined only on x E [0,4]: y 4 110 -1 -1 Compute the Fourier coefficients for f(x). For this question, we will reflect the graph around the y-axis to get an even function: 1 0 -5 13 -1 We get L =4 (x)dx A0 =
f(x) is the function illustrated below, defined only on x E [0,4]: y 4 110 -1 -1 Compute the Fourier coefficients for f(x)....
Type or paste question here
3. (20 pts.) Consider the function f defined on (0, 2) by 2+1 f(x) = = { 0<x< 1 1<x< 2 (a) Denote by fs the sum of the sine Fourier series of f (on (0,2]). Plot the graph of the function fs for x € (-2, 4), indicating the values at each point in that interval. Compute fs(0) and fs(2). [You do not have to compute the coefficients of the Fourier series.] (b) Denote...
which part b uses the answer from part a.
4. (35 pts) Let f(x) = x(1-x) for 0 < x < 1. (a) (15 pts) Compute the Fourier cosine series FCS f(x). (b) (5 pta) Find the formal solution of the problem BC u,(O, t)-u(1,t)-0, (c) (5 pts) Show that there can be no solution of problem (A) which is Ca for 0 S S 1 and (d) (10 pts) Show that there is a Co solution of the DE...
2. Let f(x) = 8 + 3x4 -1 5x<1, f(x+2) = f(x). Which best describes the Fourier series of f: (a) It is a Fourier cosine series. (b) It is a Fourier sine series. (c) It is a general Fourier series with sine and cosine terms.
solve for L, A0, An, Bn, and f(x).
f(x) is the periodic function illustrated below: y 1/0 -9 Compute the Fourier coefficients for f(x)
f(x) is the periodic function illustrated below: y 1/0 -9 Compute the Fourier coefficients for f(x)
3. Let f(x) = 1 – X, [0, 1] (a) Find the Fourier sine series of f. (b) Find the Fourier cosine series of f. (Trench: Sec 11.3, 12) (Trench: Sec 11.3, 2)
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