∑ n = 1 ∞ sin ( ( 2 n − 1 ) π x ) 2 n − 1 = π 2 ( f ( x ) − 1 2 ) for the function f ( x ) = { 0 , − L < x < 0 L , 0 < x < L which is the square wave with L = 1.

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Answer 1

Question

Chapter 10.3, Problem 19P

a.

To determine

To show: ∑n=1∞sin((2n−1)πx)2n−1=π2(f(x)−12) for the function f(x)={0, −L<x<0L, 0<x<L which is the square wave with L = 1.

b.

To determine

To show: g(x)=π2(f(x)−12)−∑n=1∞sin((2n−1)πx)(2n−1)(1+(2n−1)2) converges much faster than the series simplify the function.

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Q2 H let x(+) = &cos (Ait+U) and. 4(+) = ß cos(12t +V), where d. B. 1. In Constants and U,V indep.rus have uniform dist. (-π,π) Show that: ①Rxy (+,4+1)=0 @ Rxy (++) = cos [ when U=V Q3 let x(t) is stochastic process with Wss -121 e, and Rx ltst+1) = ( 2, show that E(X) = E(XS-X₁)² = 2(-1). Qu let x(t) = U Cost + (V+1) Sint, tεIR. where UV indep.rus, and let E (U)-E(V)=0 and E(U) = E(V) = 1, show that Cov (Xt, Xs) = K (t,s) = cos(s-t) X(+) is not WSS.

Answer 2

Question

Chapter 10.3, Problem 19P

a.

To determine

To show: ∑n=1∞sin((2n−1)πx)2n−1=π2(f(x)−12) for the function f(x)={0, −L<x<0L, 0<x<L which is the square wave with L = 1.

b.

To determine

To show: g(x)=π2(f(x)−12)−∑n=1∞sin((2n−1)πx)(2n−1)(1+(2n−1)2) converges much faster than the series simplify the function.

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Answer 3

Question

Chapter 10.3, Problem 19P

a.

To determine

To show: ∑n=1∞sin((2n−1)πx)2n−1=π2(f(x)−12) for the function f(x)={0, −L<x<0L, 0<x<L which is the square wave with L = 1.

b.

To determine

To show: g(x)=π2(f(x)−12)−∑n=1∞sin((2n−1)πx)(2n−1)(1+(2n−1)2) converges much faster than the series simplify the function.

Expert Solution & Answer

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Answer 4

Question

Chapter 10.3, Problem 19P

a.

To determine

To show: ∑n=1∞sin((2n−1)πx)2n−1=π2(f(x)−12) for the function f(x)={0, −L<x<0L, 0<x<L which is the square wave with L = 1.

b.

To determine

To show: g(x)=π2(f(x)−12)−∑n=1∞sin((2n−1)πx)(2n−1)(1+(2n−1)2) converges much faster than the series simplify the function.

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Answer 5

Chapter 10.3, Problem 19P

a.

To determine

To show: ∑n=1∞sin((2n−1)πx)2n−1=π2(f(x)−12) for the function f(x)={0, −L<x<0L, 0<x<L which is the square wave with L = 1.

b.

To determine

To show: g(x)=π2(f(x)−12)−∑n=1∞sin((2n−1)πx)(2n−1)(1+(2n−1)2) converges much faster than the series simplify the function.

Answer 6

Chapter 10.3, Problem 19P

a.

To determine

To show: ∑n=1∞sin((2n−1)πx)2n−1=π2(f(x)−12) for the function f(x)={0, −L<x<0L, 0<x<L which is the square wave with L = 1.

Answer 7

Chapter 10.3, Problem 19P

a.

To determine

To show: ∑n=1∞sin((2n−1)πx)2n−1=π2(f(x)−12) for the function f(x)={0, −L<x<0L, 0<x<L which is the square wave with L = 1.

Answer 8

b.

To determine

To show: g(x)=π2(f(x)−12)−∑n=1∞sin((2n−1)πx)(2n−1)(1+(2n−1)2) converges much faster than the series simplify the function.

Answer 9

b.

To determine

To show: g(x)=π2(f(x)−12)−∑n=1∞sin((2n−1)πx)(2n−1)(1+(2n−1)2) converges much faster than the series simplify the function.

Answer 10

Expert Solution & Answer

Answer 11

Expert Solution & Answer

Answer 12

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Answer 13

Ch. 10.1 - In each of Problems 1 through 13, either solve the...Ch. 10.1 - Prob. 2P Ch. 10.1 - In each of Problems 1 through 13, either solve the...Ch. 10.1 - Prob. 4P Ch. 10.1 - In each of Problems 1 through 13, either solve the...Ch. 10.1 - In each of Problems 1 through 13, either solve the...Ch. 10.1 - In each of Problems 1 through 13, either solve the...Ch. 10.1 - Prob. 8P Ch. 10.1 - Prob. 9P Ch. 10.1 - In each of Problems 1 through 13, either solve the...

∑ n = 1 ∞ sin ( ( 2 n − 1 ) π x ) 2 n − 1 = π 2 ( f ( x ) − 1 2 ) for the function f ( x ) = { 0 , − L &lt; x &lt; 0 L , 0 &lt; x &lt; L which is the square wave with L = 1.

To show: ∑n=1∞sin((2n−1)πx)2n−1=π2(f(x)−12) for the function f(x)={0, −L<x<0L, 0<x<L which is the square wave with L = 1.

To show: g(x)=π2(f(x)−12)−∑n=1∞sin((2n−1)πx)(2n−1)(1+(2n−1)2) converges much faster than the series simplify the function.

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Chapter 10 Solutions

∑ n = 1 ∞ sin ( ( 2 n − 1 ) π x ) 2 n − 1 = π 2 ( f ( x ) − 1 2 ) for the function f ( x ) = { 0 , − L < x < 0 L , 0 < x < L which is the square wave with L = 1.