01000MA 101032103

Pages: 3
Reg No.: Name:
APJ ABDUL KALAM TECHNOLOGICAL UNIVERSITY
B.Tech Degree S1,S2(S,FE) Examination May 2021 (2015 Scheme)
Course Code: MA101
Course Name: CALCULUS
Max. Marks: 100 Duration: 3 Hours
PARTA
Answer all Questions. Each question carries 5 Marks Marks
1 a) ⋅ ⋅∞≴⇂⋯ (2)
Determine whether the series ‏مز‎ (=) converges.
0) Find the Maclaurins series of f(x) = ன்‌ (3)
2 022 ച ‏ج02‎ _ 22 2
2) Prove that ह = न where z = x“y. (2)
b) Compute the differential dz of the function z = ‏سے‎ (3)

3 ஐ Find the velocity and acceleration of a particle moving along a circular path (2)

F(t) = 2costt + 2sintf at time ர்‌ = nm

b) एत the directional derivate of f(x,y, 2) = x?y — yz? +z at the point (1,-2,0)1௩ (3)

the direction of the vector @ = 28+ | - 2

4 2) Evaluate fo fo 7 ext¥ +2 dxdydz (2)
b) Find the area of the region enclosed between the parabola y = x? and the line (3)

y = 2x.
5 9) Find the divergence and curl of 7 = xf + yf + zk. (2)

0) Find the work done by the force field F(x, y,z) =xyt+yzf+xzk on a particle (3)
that moves along the curve C:7(t) = ಣಿ) 3k, (0
6 8) Evaluate by Green’s Theorem, ಕ್ಕೆ ydx + xdy where 0 is the unit circle. (2)

b) Use Divergence theorem for F(x,y,z)=xt+yf+zk taken over the cube (3)
bounded by the planes x = 0,x =1,y=0,y = 1, 2 = 0 10 2 = 1.

PART B
Module I
Answer any two questions. Each question carries 5 Marks
7 7 படட ‏ہس‎ 5
est the convergence of —> ಧಾರಾ” (5)
7

8 Find the Taylor series expansion of f(x) = cosx;x तिः (5)

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