Suppose f(x, y) 13-6x² +10xy — 12y² + .. is the multivariate power series expansion of ƒ centered at (0,0). Is (0,0) a critical point for f? If so, classify (0, 0) as either a local minimum, maximum or saddle point. =
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- Dynamics problemFind the trigonometric Fourier series for the square 2n-periodic wave defined on the interval [-11,1]: f(x) = {0, if-SX<0 f(x) = {1, if 0Let X have pdff(x) = e-X /(1+ e -X)2 −∞< x < ∞Show that Y = 1/(1+ e -X)has the uniform distribution U(0,1). State the method you use and show allwork.Do it Quickly Asap 30 minsExpress f(x) = |x| Fourier series. Hence obtain -TSubject: calculusFind the fourier analysis and plot the first 5 partial sums: 9. f(x) 10. f(x) = = X if -TThe Fourier series of f(x) = x in the interval -t < x < T is %3D 1. f(x) = 2 sin x - sin 2x + ... 2. f(x) = sin x + sin 2x + .. sin 2x 3. f(x) = sin x +... 2 - sin 2x 4. f(x) = 2 sin x +...2) For a random variable X, its kth-order moment is defined as E(X*). Given the p.d.f. fx(x) of X, its Fourier transform Fx(u) = S fx(x)e¬j2muz dx is also called moment generation function. a) Determine an expression of E(X*) in terms of Fx(u). Hint: consider the kth-order derivative of Fx (u) with respect to u and examine its relationship to the definition of E(X*). b) If X is N(0, o²), we know that Fx (u) = exp (-}(2u)°o²). Apply the above idea to determine E(X3) and E(Xª) in terms of ơ².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,