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12

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. Find the radius of convergence and interval of convergence of the 507053. 1

FIRST SEMESTER B.TECH DEGREE EXAMINATION, JANUARY 2016
Course Code: 1
Course Name: CALCULUS
Max. Marks: 100 Duration: 3 Hours
PART A
Answer all questions, each question carries 3 marks

cosk

00
Show that the series 3
k=1 k

Find (ടം 8
dx

is convergent.

Identify the surfaces 5x? —4y? + 2022 =0
Equation of a surface in spherical coordinates 15 ‏م‎ = sin@sing
Find the equation of this surface in rectangular coordinates.
Given f = © siny; show that the function satisfies the Laplace equation fx + fy =0

ct w=4x2 2,,2 −∙ −∙ ∙ ∙ “3 ow
Let # = 4.८^ + 4}~ +~ .where x=psingcosé, } = @ भा कओ 6, z=pcosg Find 7

४ ‏م‎

using chain rule.
A particle moves along a circular helix in 3-space so that its position vector at time t is
r(t) = (4९05 2 t)i+ (4sinzt)j+tk Find the displacement of the particle during theinterval
15155
Find the tangent to the curve 16) = (t?~ Lit tj at (= 1

5 @ pb dydx
valuatef, ‏ہل‎ ന്നി

The line y 2- x and the parabola y = x’ intersect at the points (-2, 4) and (1, 1).If R is the

region enclosed by y=2-x and ടാ sthen find y)dA
R
(10 x 3 = 30 Marks)
PART 8

Answer any 2 complete questions each having 7 marks 1
&-5) ¢
k2

3

. Test the convergence of ‏سس سے‎ ப்ப
12 23 ॐ

Find the Taylors series of = 1.