Reg No.:

Max. Marks: 100

1 2)
b)

2 a)
b)

3 a)
b)

4 2)
b)

5 ஐ
0)

6 a)
0)

7

8

9

A1100

APJ ABDUL KALAM TECHNOLOGICAL UNIVERSITY
FIRST SEMESTER B.TECH DEGREE EXAMINATION, JULY 2018
Course Code: 1
Course Name: CALCULUS

PART A
Answer all questions, each carries 5 marks
Express the repeating decimal 1.454545....as a fraction.

Expand f(x) = sinmx using Taylor series about x = न

Find the slope of the surface 2 = y3x+2y in the x-direction at the point (1,3).
Find a linear approximation of f(x, 9, 2) = x” —xy+3sinz at the point (2,1,0).
Determine whether 7(1) = 3517 11 + 3tj is continuous at t = 0.

Find the gradient of f(x, y) = ४८? at (1,0).

പ്ല ட dy

0 2 logy
Using double integral find the area bounded by x= y’,x+y=2 in the positive
quadrant.
Find the divergence of vector field 7 = य +2xyj.

Show that the vector field F = 2x(y? + 2] + ಏಣಿ) + 32226 is conservative.

Evaluate

Locate sources or sinks of F = xyi - ‏زور2‎ + yk.
By Green’s theorem evaluate ദ: yydxt+(2x+y)dy, ಲಿ is the circle
2

PART B
Module I
Answer any two questions, each carries 5 marks
Determine whether ‏ےپ‎ is convergent.
far (3k -1)(3k +2)

Test the convergence of 1 Paes ന + ‏سو ا قوط‎
3! 3! 7!

Expand f(x) = i in powers of (x-2). Find the interval of convergence and radius
೫

of convergence of the power series obtained.

Page 1 of 3

Duration: 3 Hours

Marks

(2)
(3)

(2)
(3)
(2)
(3)
(2)

(3)

(2)
(3)
(2)
(3)

(5)

(5)

(5)