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    Dirichlet's theorem on both types of discontinuity

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    a) Sketch the periodic function y=ex, ‐2< x <2 and y(x)=y(x+4) for
    values of x from ‐6 to 6.
    State the period and whether the function is odd even or neither
    b) give the Fourier series for the odd periodic extension of: y=ex, 0< x <2
    c) Confirm Dirichlets theorem on both types of discontinuity

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    https://brainmass.com/math/fourier-analysis/dirichlets-theorem-both-types-discontinuity-432107

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    a) Sketch the periodic function y=ex, -2< x <2 and y(x)=y(x+4) for values of x from -6 to 6. State the period and whether the function is odd even or neither.
    b) Give the Fourier series for the odd periodic extension of: y=ex, 0< x <2
    c) Confirm Dirichlet's theorem on both types of discontinuity

    Solution:

    a) Since it is given that , the period is T = 4. We will plot the graph of and this graph will be repeated on (-6, -2) and (2, 6), according to the figure below:

    Relevant intersections:
    Since the graph shows no symmetry ...

    Solution Summary

    Dirichlet's theorem on both types of discontinuity is clearly reinforced.

    $2.19

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