Page 1 :
Practise questions, , Section A Short type questions:, , Define the periodic function., , Define Fourier cosine series, , Find the first order partial derivative of, , ()u=e*cosy (ii) u= tan {|, , , , , , Find a, in Fourier series for f(x) = x°-x: - 1 <x < 17, , State Euler’ s theorem for homogeneous function, Find the first order partial derivatives of u = e” cosy, , Xicw<x<t, , , , Find a, in Fourier series for f(x), , Section B type questions:, , , , Ifu= f(r), where then prove that, , FU, FU _ pq 4], ae tay hort, , Find the half — range cosine series for f() =x, O<x <1, Find the half — range sine series for f(x) = 2x-1, 0<x<1, , Develop the Fourier series representation for the function f(x) =e”,, O0<x<2n, , Find the volume of the greatest rectangular parallelepiped inscribed in the, xy Zz, , S4O45=, , ap to!, , Find the minimum value of u= x+y +z? when ax + by + cz =p., , ellipsoid whose equation is, , Section C type questions, , y=2, ay ~(clog(ex))"!, , Ifxyiz? =, , , , , , , Show that at x =, , , , Find the maximum value of u, where u = sinx siny sin (x + y), , Find the maxima and minima of u= x'y°(1-x- y), , Find the Fourier series of the function f(x) = x + x’ in the internal (~ Tr, 17) and, w 1,1, Weiy4i,45, , show that “G=1+ 55+ 3, , Prove that, , where x = Ecos a-nsin a, y=Esin atncos a