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Max. Marks: 100

1 a)
b)
2 9)
b)
3 a)
b)
4 2)
b)
5 ஐ
0)
6 a)
0)

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APJ ABDUL KALAM TECHNOLOGICAL UNIVERSFF¥

B.Tech examinations (5) September 2020 51/52 (2015 Scheme)

Course Code: 4101
Course Name: CALCULUS

PART A
Answer all questions, each carries 5 marks.

k+2
Determine whether the series 3, 6 converges. 1150, find the sum
Find the Maclaurin series expansion of f(x) = /௩(1- x)up to 3 terms
ಗ್ಗ 23 az; ೫
Find द and ay if ye* —5cos2z = 32
Use chain rule to find ക at (0,1,2) forw =xy+yz, y=sinx,z = €>.

Find the velocity of 8 particle moving along the curve

1 117 te! ೦೦೩1) 18 att=n

F(t) == €
Find the unit normal to the surface yz+zx+xy=c 21 (-1,2,3)

2 3-9

Evaluate [ 1 dx dy
1 ந

| dy ۴

2
وت و[ | ‎Evaluate‏

Find the value of constant a so that if

F = (3x - 2) + 2) ‏غ‎ + (4x ~ ‏بيه‎ + 2([ +(x ‏برح‎ + 22(1 15 solenoidal.

Find the work done by a force field F(x, ೫) = —yi+ xj acting on a particle
moving along the circle x? + y? = 3 from (V3, 0) to (0, V3)

Determine the source and sink of the vector field F(x, 9, 2) = 200 — 2x)i+

208 - 2y)j + 2(z3 - 2277

Using Stoke’s theorem prove that ८ 7.67 =Owherer=xit+tyj+zk and

C is any closed curve.

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Duration: 3 Hours

Marks

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