20.

21.

22.

23.

24.

25.

26.

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3 D 31818

3 (-1)” 227

(a) Find the radius of convergence and interval of convergence of the series 2 ` छम
7 = 0 .

(b) Find a power series representation of log ( 1 —x) on (-1, 1).

Sketch the curve described by the parametric equations x = t? — 4, உ: 6> ‏ہے‎

Find an equation of the plane containing the points P(3,-1,1), Q(1,4,2) and R(0,1,4).

. 12. 1
Find the curvature of the twisted cubic described by the vector function 7(¢) = ti + i” 2+ gtk

Section C

Answer any number of questions from this section.
Each question carries 10 marks.
Maximum marks : 20.

1 x
(a) Evaluate lim [+] .
മഥ x

(b) A power line is suspended between two towers. The shape of the cable is a catenary with

x
equation Y= ഇ
cable.

(a) Show that | e* dxig convergent.
0

li n!
(b) Find im —

noon” *
(a) Find the Taylor series for f(x) =sinx at x= 1/6.
(b) Find the area of the region enclosed by the cardioid ; =1+cos0.-

(a) Identify and sketch the surface 12x? —3y? +427 +12=0.

(b) A particle moves along a curve described by the vector function r(t) = ti+ #7 +k. Find the
tangential scalar and normal scalar components of acceleration of the particle at time t.

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