the Fourier series for the following functions f(x)= x² when 0< x < 2 f(x) = x =2A-x if 0 ≤x≤T if π ≤x≤ 2π. f(x)=0 for - < x≤0 = x for 0 < x ≤n. f(x) =x in (-7, π). I
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- b) The following function f(x) is periodic with period T = 27. Sketch the function over - 47 ≤ x ≤ 47 and determine whether it is odd, even or neither. Then, use the Fourier series expansion to represent the functions. f(x)= -6; for-2n Graph of g 6. Let g be the piecewise-linear function defined on [-27, 4x] whose graph is given above, and let f(x) = g(x) - cos %3D (a) Find f(x) dx. Show the computations that lead to your answer. -2x' (b) Find all x-values in the open interval (-2z, 4x) for which f has a critical point. (c) Let h(x) = g(t) dt. Find h'- %3DFor f (X)= -3/5+1, f (-10)=5 of 22 A large aircraft is flying on a bearing of 300° (60° west of north) with an airspeed of 500 mph. It is being affected by a 60 mph wind blowing towards the west, as shown in the diagram below. 60 mph N 500 mph 60이 W E The distance, R, as indicated in the diagram, that the plane has travelled after 1 hour is, to the nearest mile, 527 miles 553 miles O 591 miles O 493 milesQ4. Find the Fourier cosine series for the function: f(x)= 1 0 1 0i need the answer quicklyperiod -π ≤ t ≤ π. The following f(t) is a periodic function of period T = 27, defined over the -2 2 when when 0 < t ≤π -2. Show that the Fourier series function defined by f(x) below is an even function. Hence determine the Fourier series for the function: f(t)= 1-1, 1+1, when - <1 <0 when 0 <1Find the Fourier series of the function f(x), of period 1, defined by: f(x)=x^2 if 1≤x<2 Graph the solution.Recommended textbooks for youAdvanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, IncorporatedNumerical Methods for EngineersAdvanced MathISBN:9780073397924Author:Steven C. Chapra Dr., Raymond P. CanalePublisher:McGraw-Hill EducationIntroductory Mathematics for Engineering Applicat…Advanced MathISBN:9781118141809Author:Nathan KlingbeilPublisher:WILEYMathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,Advanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, IncorporatedNumerical Methods for EngineersAdvanced MathISBN:9780073397924Author:Steven C. Chapra Dr., Raymond P. CanalePublisher:McGraw-Hill EducationIntroductory Mathematics for Engineering Applicat…Advanced MathISBN:9781118141809Author:Nathan KlingbeilPublisher:WILEYMathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,