Consider the function. f(x) = { -25 x+1, -7 < x < 0 1-x, 0≤x <7' (a) Sketch the graph of f(x) for three periods fx -20 -10 f(x)= [Choose one f(x+14) = f(x) -5 10 M (b) Find the Fourier series of f(x) 15 20 25 8
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- Q2/ Find the Fourier series to represent the function f(x) given by: -1 for f(x) = 0 for +1 for I -HA periodic function f(x) is defined by f(x) = x² + 3 for –2Consider the following. -2 SxS -1, (x) -7x, -1Find the first four of the Taylor the function 1/x about the point a = -1 (Your answers should include the variable x when appropriate) 1/x = ?+?+?+? I got 1/x= -1/0!+ (x+1)/1!+-2(x+1)^2/2!+(6(x+1))/3! However, (x+1)/1! And (6(x+1))/3! Is incorrect. Please help me.Please solve the question quickly, less than 30 minutes= f(x) = { 2. Let 0 -2Q2/ The sequence {x} has the Z transform F(z) 3z(z-1) %3D z3-2z2-4z+8 Find {xg}Question 4 Let f be a function that has derivatives of all orders on the interval (3, 5). Use the values in the table below and the formula for Taylor polynomials to give the 4" degree Taylor polynomial for f centered at x = = 4: f(4) f'(4) f"(4) f"(4) f(4)(4) -4 10 8 -5 a) O-4 + 6 (x – 4) + 10(x – 4)² + 8(x – 4)³ – 5(x – 4)* b) O-5x4 + 8x³ + 10x² + 6x – 4 c) O-4 + 6 (x + 4) + 10(x + 4)² + 8(x + 4)' – 5(x + 4)* d) O-4 + 6 (x – 4) + 5(x – 4)° +x – 4° –- – 4) 5 (x- 4)* 24 4 e) O-4 + 6 (x + 4) + 5(x + 4)² + 5 x +4)° – x+4* 24 5 f) O- 24 4 + '+ 5x? + 6x – 4 3If f is the Fourier series of g(x)= √3, [16-², -4 < x < 0 then 0≤ < 4 f(2)=¯ + 2 [(0) cos (1 x) + ( ) sin (7-²)] 2 What does f(-4) equal? f(-4) What does f(-2) equal? f(-2) = What does f(0) equal? What does f(1) equal? What does f(4) equal? (0) f(1) = ƒ(4) = *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,