A B1A216S (2015 Admission) Pages:2
वद निक Name

APJ ABDUL KALAM TECHNOLOGICAL UNIVERSITY

FIRST SEMESTER B.TECH DEGREE (SUPPLEMENTARY) EXAMINATION,
PEBRUARY 2017 (2015 ADMISSION)

Course Code: MA 101
Course Name: CALCULUS
Max.Marks : 100 Duration : 3 Hours

PART A

(Answer all questions. Each question carries 3 marks)

27 9
1) Show that the series x 2 | converges.
n=l
2) Classify the surface 2 = (x -1(2 + ‏بر)‎ +2)? +3

3) Find the Maclaurin series for cos x

xy
9 ‏چس عو‎
4) Evaluate റിവാ + +

5) Convert the cylindrical co-ordinate into rectangular co ordinate of (4, 7/3 —3).

6) Find the slope of the surface 2 = xy” in the x direction at the point (2,3).

7) Find the directional derivative of ഗ്മ ye’ +z at (1,-2,0) in the direction of
न = 27 + 7422
8) Find the unit normal to the surface xy ‏وير عد‎ + wz == ‏ے‎ at (-ಟ|, 2,3)
ah
9) Evaluate 1 ர்‌ x zy dxdy
11
10) find the area of the region R enclosed by ‏ہر‎ 55३ , ‏بق‎ =2,x=O.x=—=y.

PART B
(Answer any 2 questions. Fach question carries 7 marks)

3 75 n ரீ
9

⋅ ∙∙⇁∢−∎
11) Test the absolute convergence of > ‏سو‎
‎newt
‎12) Determine the Taylor's series expansion of (டியூ sine ‏عد‎ atx 1/2.
ऊ) * ⋅ i 3 ಈ
13) Test the convergence of >>> + SS Tt ಇರರ...

3.2.3 2.3.4 3.4.35