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ence
Find the Maclaurin series of sin x and determine its interval of converg

ith the given parametric equation

Find a rectangular equation whose graph contains the curve C w
ॐ = 2 + 1, ¬ = ४ - 3.

7 7 ച १
ച ர ಸ್ನ (ಎ.
Find the equation of the tangent line to the curve * ~ sect, y = tant, 9 Find the parametric equation for the line passing through the point (-2, 1, 3) and parallel to the

vector < 1,2,-2).

The point (8 3 ಸ) is expressed in spherical co-ordinates. Find its rectangular co-ordinates.

Find the antiderivative of r) (t) = costi +e‘ j + Vi k satisfying the initial condition r(0)=i+2j + 3k.
(10 x 3 = 30 marks)

Section B

Answer at least five questions.

Each question carries 6 marks.

All questions can be attended.
Overall Ceiling 30.

Use logarithmic differentiation to find the derivative of y = (Jeosx 7

3
x
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Evaluate டைக்‌
x
Evaluate J മ്‌ മ:

ஐ

2 4
Show that the series | n(n+]) 1) ~ =| is convergent and find its sum.
az

x-2
Find the radius of convergence and interval of convergence of the series 2 ( )
17 -2
Find the Taylor series for f(x) =logx at x = 1 and determine its interval of convergence.

Identify and sketch the surface 4x -3y* -12z” =0.

Let C be the helix r(t)=2cost i+2sint j+t k,t20. Find T (1) ೫೫61 (0).

(5 x 6 = 30 marks)