1.)Determine whether the Fourier series of the following functions converge uniformly or not. a. f(x) = ex, - 1 < x < 1 b. f(x) = sinh(x), - π< x < π Answer: a)The periodic function is not continuous at ± etc., so convergence cannot be uniform.   b. Like a, the periodic function has jumps at ±π etc.

Q: A function, f(x) is defined over the interval - to π as below: { f(x) = 0, 1, -π ^.

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Q: Consider the Pecewsie continuous function { f(x) = = -2 < x < -1, −1≤ x < 0, 0 < x < 2. Without…

A: Fourier series convergence

Q: Expand the function f(x) = x sinx, as a Fourier series in the interval - < x < π.

A: Given function is  for                    here               therefore f(x) is an even…

Q: f(x) = cosh(x); -T <x< T etch the function. Determine whether it is even or odd. Expand it in an…

A: Expand the given function in an appropriate Fourier series.

Q: 2. Sketch the odd 2π- periodic extension and find the Fourier Sine Series of the function f(x) given…

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Q: ". Expand the function f(x)=|x, - T < x < A in an appropriate cosine or sine series.

A: Given that, fx=x ,  -π&lt;x&lt;π  Here, -L , L=-π,π Hence, L=π As the given function is even…

Q: if 0 < x < 2; 4-x if 2<x< 4 X 1. Expand ƒ(x) = { in a half-range (a) sine series. (b) Cosine series.…

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Q: 3. f(x) = Expand the 2π-periodic function π, 0 < x < T 2π-x, π < x < 2π in a Fourier series. In…

A: Here the function is given by fx=π,            0&lt;x&lt;π2π-x,      π&lt;x&lt;2π The 2π- periodic…

Q: 1. Expand f(x) = π 0 if 0 < x < 2² ㅠ if <x< ₁ π, 1 if in a half-range: (a) Sine series. (b) Cosine…

A: The function is defined by fx=0if 0&lt;x&lt;π21if π2&lt;x&lt;π We have to evaluate the half range…