Use Laplace transform to find the bounded solution in x > 0, t> 0 of 8²0 əx² with 20 Ət 0=2e-2 at x = 0, t > 0 0=1 at t=0, x > 0
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- Consider the function f(x) = cos(2x) for -2pi < x ≤ 2pi and zero otherwise.A) Show that it meets the condition of having a Fourier transform.B) Find it's Fourier transform F(k).C) Demonstrate that F(0) = area under the curve of f(x).Solve the ODE using laplace transformThe polynomial f= x^3- 4x + 2 is irreducible over Q. Let u be a root of f in some extension Q(u) of Q. Compute for (1 + 2u) (1 - u^2)
- Which of the following expressions' inverse Laplace transform is the solution to the initial value problem a" – 2x' + 2x = 0, x(0) = 0, x'(0) = 1 ? Lütfen birini seçin: 1 s2 + s – 2 1 s2 + 4s – 2 1 s2 – 2s + 2 s2 + 2s + 4 s2 – 2s + 45Find the laplace transform of the piecewise function: S2t y = t2 0Find the laplace transform of f (t) = 2tª – 3est + 10 cos 2t OF(s) = 7s7-20s-20s5-48s+96s2+192s-384 88-2s7+16s6-8s5 %3D 7s7-20s-12s4+48s3-192s2+96s-384 OF(s) = 58-2s7+16s°-8s5 O F(s) = 7s7-20s-12s5-48s4-96s-96s-384 58-2s7+16s%-8s5 O F(s) = 7s7-20s-12s5-48s-92s2+196s-384 s8-2s7+16s6-8s5 O F (s) = 7s7-20s-120s+48s-92s2+196s-384 58-2s+16s6-8s5 %3D O F(s) 7s-20s-12s+48s-95s2+192s-384 g8-2s7-16s6-855 %3D OF (s) = 7s7-20s6+12s-96s+48s2+192s-384 $8-2s7+16s5-855 OF (s) 7s7-20s-12s+48s-96s2+192s-384 s8 -2s7+16s6-855 %3DDetermine the inverse z-transform using partial fraction expansion that results to a causalfunction:Find the fourier analysis and plot the first 5 partial sums: 9. f(x) 10. f(x) = = X if -TRecommended 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,