Reg No.:

Max. Marks: 100

1 ஐ
b)
2 ஐ
b)
3 a)
b)
4 ஐ
b)
5 (a)
(b)
6 (a)
(b)
7

A7001

Total Pages:

Name:

3

APJ ABDUL KALAM TECHNOLOGICAL UNIVERSITY

FIRST SEMESTER B.TECH DEGREE EXAMINATION, DECEMBER 2017

Course Code: MA101
Course Name: CALCULUS

PARTA
Answer all questions, each carries5 marks.
Test the convergence of the series 2 ന |

n

Find the radius of convergence of 2
n=l 2n+ 3

Find the Slope of the surface 2 = xe~” + 5.1 in the y-direction at the point (4,0).

Find the derivative of മച്ചി with respect to ¢ along the path

x = 1021, ‏بر‎ =2t.

Find the directional derivative of f =x? y—yz* +z at (-1,2,0) in the direction of

¢ = 27 + j+2k.

Find the unit tangent vector and unit normal vector to r(t) = 46050 + 4511 fj +tk

7
att=—.
2

1௦23 2

Evaluate | | ഷ്മ

0 0

Evaluate [fo dA where R is the region bounded by the curves நற? and
R

x=y’,

Find the divergence and curl of the vector F(x, y,z) = yzi+ xy’ ‏زر‎ + 12.

Evaluate fx +y°)dx+2xydy along the circular arc © given
0

⋅ 7
x=cost,y=sin¢t for ‏ک1 ک0‎

Use line integral to evaluate the area enclosed by the ellips

Evaluate [൦ —3y)dx +3xdy ,where Cis the circle x7 + y? =4.
1

PART 8
Module 1
Answer any two questions, each carries 5 marks.

Test the convergence or divergence of the series 2 (ಎ)

n=l

Page 1 of 3

by

Duration: 3 Hours

Marks
(2)

(3)

(2)
(3)

(2)

(3)

(2)
(3)

(2)

(3)

(5)