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4൧192001 Pages:3

PART 8
Module 1
Answer any two questions, each carries 5 marks.
Test for convergence of the series Ly» = (5)
ke
Find the radius of convergence of മംഗഫ്‌ (5)

derivative.

Module 11
Answer any two questions, each carries 5 ma.
If ‏ديه‎ (Z,%,2) find the value of ‏رید‎ +2 3,

Find the local linear approximation L(x ந) of f(x VSS at the

(5)

point P(4,3).Compare the error in the approximation 10 09 L at
the point Q(3.92,3.01) with the distance between P and Q
Locate all relative extrema and saddle point for the function
f(x,y) = x3 + ‏قير‎ - 6xy 20 (5)
Module 111

Answer any two questions, each carries 5 marks.

Find the equation of the unit tangent and unit normal to the
(5)

curve x=e'cost,y =e'sint.z =e" ;att=0.

A particle moves along the curve r(t) = (2) + ध्य + ४ , where t

denotes time. Find

1) ൯൩൦ scalar tangential and normal components of acceleration (5)
at timet = 1.

2) The vector tangential and normal component of acceleration at

time t=1

Find the equation of the tangent plane and the parametric equations

(5)
of the normal line to the surface z= 4x3 2 + 2.# -2 at (1,-2,10).
Module 1५
Answer any two questions, each carries 5 marks.
Use double integral to find the area of the plane enclosed by (5)
32 =4x and x? =4y
Change the order of integration to evaluate 19 i xy dy dx (5)

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