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C 20647 (Pages : 3) வி... ௮ ಸ...

SIXTH SEMESTER U.G. DEGREE EXAMINATION, MARCH 2022
(CBCSS—UG)
Mathematics
MTS 6B 12—CALCULUS OF MULTIVARIABLE
(2019 Admissions)
Time : Two Hours and a Half Maximum : 80 Marks
Section A (Short Answer Questions)

Answer at least ten questions.

Each question carries 3 marks.

All questions can be attended.
Overall Ceiling 30.

1. Find the domain and rang of the function f(x,y)=x+3y-1.

5 e*” (sinx+cosy)
2. Evaluate യ) 1-322

3. Find /f, and i, if f (x,y) =xcosxy”.
7 ^
4, ೫170 136 61/00/07೩1 6071೩76 08 /' (೫,2) - x? sin 2y at( 13 in the direction of j = 31 -47.

5. Find Vf (x,y,z) if f(x,y,z)= x? + y? —4z and find the direction of maximum increase of f at the
point (2, -1, 1).

6. Find the relative extrema of the function f(x,y) = 2 + 2 - 2 + 4).

7. Find the volume of the solid lying under the elliptic paraboloid z = 8— 2x? — y? above the rectangular
region given by 0
8. Find the mass of the triangular lamina with vertices (0,0),(0,3) and (2,3) given that the density

at (x, y) is p(x,y)=2x+y.

Turn over

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