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A A1900

Reg No.: Name:

APJ ABDUL KALAM TECHNOLOGICAL UNIVERSITY
FIRST SEMESTER B.TECH DEGREE EXAMINATION, DECEMBER 2018

35 Course Code: 1 °
Course Name: CALCULUS
Max. Marks: 100 Duration: 3 Hours
PART A

Answer all questions, each carries 5 marks. Marks

1 8 Test the convergence ௦7212, कत (2)

b 2
) Discuss the convergence of ‏ا‎ ٦ (3)

k=l
2 a) Find the slope of the surface z = sin(y? — 4x) in the x — direction at the point

(2)
(3,1).
b) Find the differential dz of the function z = ഒന (2). (3)
3 a) Find the direction in which the function f(x,y) = xe*decreases fastest at the (2)
point (2,0).
b) Find the tangent plane to the elliptic paraboloid z= 2x7 + y? at (1,1,3) (3)
4 9) Evaluate ff, ysinxy dA, where ೫ = [1,2] × [0,7]. (2)
b 3
) Evaluate 0 4 तग्र dy dx (3)
5 ൭ ifA = (3x? + 6y)i— 14yzj + 20xz7k ,evaluate J A.d7from (0,0,0) 10(1,1,1) (2)
along the path,x = ‏ورةع = مرخ‎ =t3
b) Prove that F=(x? — yz)it (y? - xz)j + (z? - xy)k is irrotational. (3)
6 a) Determine the source and sink of the vector field (2)

F(x,y,z) = 2(x3 — 2x}it+ 2(y? — 2974 2(<7 - 22
b) Evaluate ff, F.#ids where 5 is the surface of the cylinder x2+y?=4,z=0, (3)

z=3 where = (2x - +)? + (2y - 2) + 224

PART B
Module 1
Answer any two questions, each carries 5 marks.
7 Check the convergence of the series 7+ + = + ~ + (5)
ಜ್‌
8 Find the radius of convergence of the power series 2.7 Ss (5)
9

21-14
Determine whether the alternating series ‏ہد‎ ಕೆ is absolutely (5)

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