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[Total No. of (i) PrintedPages 4 (ii) Questions 8], Sub Code :0541(1048) Exam Code .;/0006, , Exam : B.A./B.Sc. (General), 6th\Semester, Subject=:, Mathematics, , Paper : Paper-l| : Analysis-ll, Time : 3 Hours Maximum Marks : 30, , Note : Attempt five questions in all selecting two, questions from each section. All questions, carry equal marks., , 1. (a) ff x dx dy, where A is the region bounded, , by the parabolas circles :, y? = 4ax and x? = day., , (b) ff Va -x?-y* dxdy over the region bounded, , by the semi circle_x? +y? =! ax ) lying inthe, first quadrant., , 2. (a Find the volume of the tetrahedron bounded, , by the planes: - yz, x=0,y=0,z=0and a +te “ek

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2., , (b), , (a), , (b), , (a), , (b), , Sff dx dy_ dz — over the positive octant, V1-x2 -y? -2?, of the sphere x74 y2#z7 21, — “A A A, fF =yi +(x - 2xz)J - xy k, then evaluate, ff (Vx Fyn ds,where S is the surface of the, s, , sphere x?+y?+z?=a" above the XY plane., , If F=(2x7+ y? ) i+ (3y - 4x)J, evaluate, , fF. dr around the triangle, , ABC whose vertices are A(0,0), B(2,0) and C(2,1)., Apply Green's theorem in plane to evaluate, , f [(2x?- y?) dx + (x? + y? )dy] , where C is the, , C, , boundary of the surface enclosedsbythe x, axis and the semi circles, y= vi-X, , Verify. Stokes THpasem for, , F 2(2x-y) i i? - yz) - -y’z K where Si is the upper, Half surface of the sphere x?+y?7+z?=1, , and C is its boundary.

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(a), , (b), , (a), , (b), , (a), , Show that the Sequence {f, (x)} defind by, f,(x) =nxe™”, converges point wise but not, uniformly in [0, 0°], , Use M,, — Test to show that the sequence, , nx, , {f, 0}, where f, (x) = 22 does not, , converge uniformly on [0,1]., , , , , , , , Show that the series, 2x 4x? 8x’, + + sccsscessseseeesesee, 1+x? 14x! 14+x®, , converges uniformly for -1 <x <1., , < 1, Show that the series > 24 nt y2, — n’t+n’x, , is uniformly convergent for all x and it can, she differentiated term by term., , Find the radii of convergence. of the, following power series, , n, Xx, , rhe