A

9

16

17
18

B1A004 (2016)

PART B
(Each question carries 3 Marks)

Answer any TWO questions

4k3-6k4+5
Test the nature of the series ve ರ್ಯಾ
६-1 81८7 +1-8

⋅ % ⋅
∁∣↿∊∁⇂⊔↿⋁∣↿∁∐↿∊↥⇀↧⇂↿⋐≗⋅∁↥⋅∣∁⊱∑∣⊂∞−−⇆∊−↥⊃∣≴≁↕ a 8 absolutely convergent or

not.
Find the radius of convergence and interval of convergence of the series
27 (൧-5

7 جا 1ےا

Answer any TWO questions
du , du , 0४

Ifu= -2,2- 7 −−−−−−

⇅∫↻↗∑⋅ ∝⋅⊃∊⊃∣⊃⋮⊑≻↾∘⋁∁↥↾↿∂≖ ಗಟ 7 +॑ 5५ 0

A function f(x,y) = x? + y*; is given with a local linear approximation
1 (८, +) = 2x + 4y—5 to f(x, y)at a point P. Determine the point P.
Find the absolute extrema of the function f(x,y) = xy - 42 on र
where R is the triangular region with vertices (0,0) (0,4) and (4,9).

Answer any TWO questions

Evaluate the definite integral Sy (eit ९7१1 + 2४६ k)dt.
Find the velocity, acceleration, speed, scalar tangential and normal

components of acceleration at the given t of
7(() = 38011 + 2costj ~ sin2tk;t= न

Find the equation of the tangent plane and parametric equation for the
normal line 10 the surface 2 = 4x%y? + 2y — 2 at the point (1,-2,10)

Answer any TWO questions

E ⋅ 4 ‏4م‎ ೩ ⋅ ⋅−
⊲⋁⊟⇂⊔∂∁∁⇂⊦↿⊜⋯↥⊜≝⊺∂∣∫⊖ 7 ஷா 1 by first reversing the order of
integration.
Evaluate ff ர்‌ “ற dzdxd

0 y? 0 ‏لا‎

Find the volume of the solid in the first octant bounded by the co-ordinate

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