A A192001
Reg No.: Name: ‏لله سرت‎
APJ ABDUL KALAM TECHNOLOGICAL 7۳
FIRST SEMESTER B.TECH DEGREE EXAMINATION(S), DECEMBER 2019
Course Code: 1
Course Name: CALCULUS

Max. Marks: 100 Duration: 3 Hours
PARTA
Answer all questions, each carries 5 marks. Marks
1 ஐ Find the sum of the series 27-4 त्न (2)
0) Determine whether the alternating series ‏ورگ‎ ತತ ನ converges. (3)
2 ച Find the slope of the function f(x,y} = xcos(xy) + ysin(xy) at (೫,1) (മു

along the x- direction.

b) ‏جج ۶ا‎ f(x?-y?), show that
az az 1 (3)
7 an +x ay =
3 a) Find lim,)7r(t), where #(६ = (1+ ಬೈನೆ, =) (2)
b) Find the directional derivative of f(x,y) = ‏کہ‎ cosy at P(0,n/4) in (3)
the direction of negative Y-axis
4 a) 111
Evaluate [| (6352752 dx dy dz (2)
000
b) Evaluate ۳ + y? कक where R is the region taken over the first
R 3
(3)
quadrant for whichx+y<1.
5 a) Find the divergence of the vector field
2
F(x,y,z) = x*yit 273213432೬ (2)
0) Evaluate | ‏برهت‎ + ydx where C is the path ೫ = x from (0,0) ೧)
to(1,1)
6 a) Determine the source and sink of the vector field
F(x, y,z) = 2(x3 - 2x)it 2(y? - 2y)j + 2(23 - 22% (2)
b) If 5 is any closed surface enclosing a volume ۷ and if
A=axi+byj+czk provethat ff Ands=(atbt+c)}V (3)

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