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Pune University - SY BSc (Sem - I) MATHEMATICS - I, April 2010

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Total No. of Questions : 4] P258 [Total No. of Pages : 2 [3717] - 101 S.Y. B.Sc. (Sem. - I) MATHEMATICS - I (51111) Calculus of Several Variables (New Course) Time : 2 Hours] [Max. Marks : 40 Instructions to the candidates : 1) All questions are compulsory. 2) Figures to the right indicate full marks. Q1) Answer the following questions. lim [10] x 2 y2 , if exists. x4 + y4 x2 y2 a) Evaluate b) If the function f(x, y) = log (x2 + y2 2 x 2 y + 6) is continuous at the point (2, 1), find f(2, 1). c) State sufficient conditions for f(x, y) to be differentiable at (a, b). d) Find x e) If f(x, y)= | x | + | y |, show that fx(0, 0) doesnot exist. f) If f(x, y) = log (x + y) and x = t2, y = 1 t2, find g) Find Jacobian J = h) State Maclaurin's theorem for function of two variables. i) Show that (1, 1) is a stationary point of the function f(x, y) = xy + ( x , y ) ( 0,0 ) f f + y , where f(x, y) = sin 1 x y ( x, y) ( u, v ) x y x + y . df . dt , where x = u uv, y = uv. 11 +. xy 1x j) Evaluate e yx d y d x. 00 P.T.O.

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Additional Info : S.Y. B.Sc. Mathematics (Semister - I) : Calculus of Several Variables (Paper - I) (New Course), Pune University
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