^ 014004

॥ 3 NAM ಟಾ

Max. Marks: 100

(b)

(b)
3 (a)
(b)

(b)

(b)

(b)

APJ ABDUL KALAM TECHNOLOGICAL UNIVERSITY

FIRST SEMESTER B.TECH DEGREE EXAMINATION, DEC 2016

(2016 ADMISSION)

Course Code: MA 101
Course Name: CALCULUS

PARTA
Answer ALL questions

k+2
3 ⋅ 3 ⋅ ⋅
↿⊃⊜↥⊜⇈⋯⊓∁⋁⋁↾↿∁⇂↾↿⊜↾⋔∁≲⊜∥⊜⊱∑∣⊂∘∘∶↥ 8 converges and if so, find its

sum.
Find the Maclaurin series for the function xe~

ج02
‎x’, then find ——‏ 11
‎Oxdy‏

Compute the differential dz of the function 2 == tan7*(xy).

Find the domain of r(t) = (V5t + 1,t?), to = 1 andr(tg)

Find the directional derivative of f(x,y) = 020 at P(5,0),in the
direction of u= ಇತ್ತಿ! + 3

E 1 ‏1م‎ dxdy
valuate ‏سس چس ہس‎
‏0ی و‎

Use double integration to find the area of the plane region enclosed by the
givencurves y= sinx and y=cosx for 0 > ‏د‎ ಹೆ

Confirm that p(x, ೫,2) = ८2 — 3y? + 425 isa potential function for
F(x, y,z) = 2xi —6yj +12 22.

Evaluate | F. dr where F(x, y) = sinx i + cosx j where © is the curve
(1) = 7 + ‏,نز‎ 0 > > 2

Using Green’s theorem evaluate 6 ydx + xdy, where © is the unit
circle oriented counter clockwise.

If ठ is any closed surface enclosing a volume V and = 2xi + 2yj +
32% , Using Divergence theorem show that 0 ‏ل‎ ۴۰٠ 05 = 77

Duration: 3 Hours

(2)

(3)

(2)

(3)