10105
Reg. No.: Name:
APJ ABDUL KALAM TECHNOLOGICAL UNIVERSITY
FIRST SEMESTER B.TECH DEGREE SPECIAL EXAMINATION, AUGUST 2016
Course Code: 184101
Course Name: CALCULUS
Max. Marks: 100 Duration: 3 Hours
PART A

Answer ALL questions. Each question carries 3 marks
1. Find derivative of y = sinh (4x-8)
2. Test whether the series converges or diverges, 9.1 232

3, Identify the surface 25 y? — x?

4. Convert from rectangular to spherical co-ordinates, (2V3, 2, -4)

OZ 092
5. Find and — if Z=cos (൧൯)

Ox oy
2 2
6. Show that 02 _ 02 if z=xy+ 593
ಡಿಡಿ ൭൭:

7. Evaluate ‏تک‎ (2tt + 38+

8. Find the arc length of the parametric curve x=e', y=e" ‏ے2‎ v2t 055 1.
9. Evaluate ] (40-20 xy ) dy dx
10. Evaluate ழ்‌ ۳ ‏وآ‎ (xyz ( 1× dy dz
PART B
Answer any 2 compiete questions each having 7 marks

0

k(k+3)
‏ہےپر‎ 0419 (7-2) (೯5)

11. Test the convergence of the series 2
12. Show that sinh” x = Inbe + Vx? +1 +1)
1
13. Find the Taylor series of - about x =1.
7+2

Answer any 2 complete questions each having 7 marks

14. Express the equation ~ - y*—z°=0 in த नि 172166.
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