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00000MA101121804

PART B
Module 1
Answer any two questions, each carries 5 marks.
k
7 ⋅⋅ −∑⋈ k
est the convergence of the infinite series 2,4൨൮ (~) ⋅
⋅ (k+4)!
Examine the convergence ० 2४-७० സിന്‌

7 ∙ ⋅ ⋮≍−⊰∣∡
⊦⇁⋯⊄⋔⊜↾∂⊄⋯≊∘∱∁∘⊓⋁∁↾⊑⊜⋂∁⊜∘⋮↧∤≖⊜⇂⊃∘⋁∨⊜↾∋⊜⊓⊜≤∑⇂≖∽∶↥ न

Module 11
Answer any two questions, each carries 5 marks.

The height and radius of a circular cone is measured with errors of atmost
3% and 5% respectively. Use differentials to approximate the maximum

percentage error in calculated volume.

− − 02
If u = ‏برع تر‎ (இ) ‏01و26 ہر-‎ 1 , find aay
Find relative extrema and saddle points, if any, of the function f(x,y) = x3. +
+#3 — 1529.

Module 11]
Answer any two questions, each carries 5 marks.

Find where the tangent line to the curve r(t) = 6072 + costj+3sintk at
the point (1,1,0) intersects the YZ plane.
Find the position and velocity vectors of the particle given
a(t)=(t 1)72] -€ 201८, ५(0) = 31-] , r(0)=k
2 2

A particle moves along acurve x = 21 ) = {~ —4t,z=3t—5 where 115 the
time. Find the component of acceleration at time t = 1 in the direction of
7 -3 +7

Module 1V
Answer any two questions, each carries 5 marks.

Evaluate fff, xysin 2 dV where 8 is the rectangular box defined by

05%5105)51 05253

2
Sketch the region of integration and evaluate ற்‌ 8 dx dy by changing the

order of integration.

Use double integral to find the area bounded by the x — axis

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