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SY.Bsc SemI(2013 Pattern)

82 pages, 86 questions, 0 questions with responses, 0 total responses,

Ankush Lavhate
Savitribai Phule Pune University (SPPU), Pune

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Total No. of Questions : 4] P177 SEAT No. : [Total No. of Pages : 2 [4717] - 5001 S.Y. B.Sc. (Semester - I) MATHEMATICS MT - 211 : Multivariable Calculus - I (2013 Pattern) (Paper - I) Time : 2 Hours] Instructions to the candidates: 1) All questions are compulsory. 2) Figures to the right indicate full marks. [Max. Marks : 40 ) Q1) Attempt any FIVE of the following: a) [10] Describe the domain and sketch it for the function f ( x, y ) = y x 2 . 2 f find . x y b) If c) State the Increment theorem for functions of two variables. d) Find the equation of normal line at the point e) x 21= x3 22 1 2 2 xyyf3,5, =(+x1,3x,yi y+41, u(P ) )6=2zj)x =cos 218 2 y +x 2ye + ,y 2 ( y 2 2 ) ( ) 0( x=0 y =2 z= dz1 dy dx Find the critical points of the function on the surface . f) Find the area of region R bounded by quadrant. g) Evaluate and in the first . Q2) Attempt any Two of the following: a) x3 xy 2 , if it exists. Evaluate ( x , ylim ) ( 0,0 ) x 2 + y 2 b) Find the derivative of f ( x, y, z ) = xy + yz + zx at direction of . [10] in the . P.T.O.

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