QUESTION 5 (15 MARKS) Let ={₁ f(x) = f(x + 2x) (i) Sketch the graph of f(x) over the interval -3

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Question 5 15 Marks Let F X F X 2x I Sketch The Graph Of F X Over The Interval 3 X 3m F X Subject T 1 (30.74 KiB) Viewed 23 times

QUESTION 5 (15 MARKS) Let ={₁ f(x) = f(x + 2x) (i) Sketch the graph of f(x) over the interval -3 <x<3m. f(x) = subject to nil (ii) Show that the Fourier series of f(x) is -2 म f(x) = +((-1)" - 1) cos nz + (-1)"+¹ sin nr. n where (9 marks) (iii) Use the result in (ii) and with appropriate value of x. find the approximate sum of the infinite series ди Ət 0, лх. 1+ = 4 b₁ = -TAX<( 0<x<* 1 3² 4 NT QUESTION 6 (20 MARKS) (a) A uniform rod of length 10 meters is held at both ends. The temperature u(x, t) at any time t of a point P which is a distance away from any of the two endpoints is 0x²¹ 1 + 1 7² 0<x< 10, t>0 u(x,t) = Σ ' sin ( N=1 u(0.t) = 0 u(10, t) 0 u(x,0) = 2-x. Use the method of separation variables to show that the general solution is given by (2 marks) NTI 10 (4 marks) (1+4(-1)"), n=1,2,3,...