A1100

Reg No.: Name: ‏رج‎

Max. Marks: 100

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APJ ABDUL KALAM TECHNOLOGICAL UNIVERSITY ۱
FIRST SEMESTER B.TECH DEGREE EXAMINATION (S), MAY 2019

Course ೧೮೦6: 184101
Course Name: CALCULUS

PART A
Answer all questions, each carries 5 marks.

“0
ies 52 ತ)
Check the convergence of the series (a=

5 . ⋅ −↧
Find the Maclaurin series of f(x} = Taw UP to 3 terms
⋅ a
2 = (32 — 2y)4, find ತ್‌

lf w = log (tanx + வாது + tan 2) then prove that
5 ow 5 ow ⋅ 222५ ட
sin 22 ‏رم‎ + sin 2y py 31122 - 2
Find the speed of a particle moving along the path x = 26050, y= 28101, 2 24

att = 7/2
If y'(t) 6550 (ರ್ಥ ಸಗರಾರಕಾಕ್ರಾರ್ಯಾಾ7-1೧6 (ಬ). ‏جح‎

Evaluate | ലു

2 کی
‎dy dz dx‏ 0 1

2 2೩
Evaluate ff xy dx dy over the area bouaded by the ellipse = + = =] and lying
in the first quadrant.
Show that F(x,y) = 2xy3i + 3x?y?j is conservative.

∙−⇀∙ − 7
8 7-1 + ‏ع + رمز‎ andr ಇ |7|, prove that Vig =0
r

Evaluate by Stoke’s theorem ಕೈ (e* dx + 2y dy — dz}, where Cis the curve

ॐ2 + > ‏2ع 2 به‎
Using Green’s theorem evaluate Se x dy —y dx where C is the circle x2 +y? = 4

PART 13
Module 1
Answer any two questions, each carries 5 marks.

1 سے
‎Test for convergence of the series Sig=1 ಜ್‌‏

Find the radius of convergence and interval of convergence of the power

ச்‌
⋅ ಪಾ
series ‏فحت طبر‎ .

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Duration: 3 Hours

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