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x? 5
Show that the series 2.൬൩ (=) is convergent. 0)
Module 11
Answer any two questions, each carries 5 marks.
Letw = fixity? + 22 where ‏عد‎ — cos6,y — sin6, 2 - [email protected] = at (5)

0 प्र , using chain rule.
Find the local linear approximation L(x,y) to f(x, y} =In (xy) atthe point (5)
P(1,2). Compare ‘the error in approximating ‏گر‎ by 2 at the point Q(1.01,2.01)
with the distance between Pand 0.
Find relative extrema and saddle points, if any, of the function (5)
f(xy) =axyti+e ⋅
Module 111

Answer any two questions, each carries 5 marks.

म्भे

Find the unit tangent T(t) and. unit normal அழு to the curve (5)
x=acost, y=asint, z=ct 820

Find the velocity and position vectors of the particle ,if the acceleration vector (5)
a(t})=sintitcostjte'k ; ೪(0) ಇಸಿ; r(0)=—itk.

Find the equation of the tangent line to the curve of intersection of surfaces (5)

z=x? + yand 3x74 297 + ‏2ع‎ = 9 and the point (1,1,2).

Module 1V
Answer any two questions, each carries 5 marks.
தத ಚ್‌ (5)
Evaluate by reversing the order of integration | | x dx dy
0 y

Evaluate ‏مهنود‎ , where R is the sector in the first quadrant bounded by (5)
R

y=vx, y=6-x, y=0
Evaluate மீ {> {८ x dz dx dy (5)

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