Question 1(a): The parametric equations of a function are x = 2 cos³0, y = 2sin 30. Question 1(b): Find the equations of the tangent and normal at the point for which 元 0=== 45° 4 (15) Find the radius of curvature and the coordinates of the centre of 2 curvature of the curve + 25 16 1 at the point (0, 4). (20) Question 2(a): Determine the smallest positive value of x at which a point of inflexion occurs on the graph of y = 3e3* cos(3x-6). (15) Question 2(b): Question 3(a): (i) Determine whether the following series is convergent or divergent: 2 2 2 2 2x3 3x4 4x5 5x 6 sin x cos x (ii) Evaluate: Lim (10) (10) If the 7th term of an A.P. is 22 and the 12th term is 37, find the first five terms of the series. (10) Question 3(b): By the use of Maclaurin's series, show that tan x=x- + 5 (20)
Question 1(a): The parametric equations of a function are x = 2 cos³0, y = 2sin 30. Question 1(b): Find the equations of the tangent and normal at the point for which 元 0=== 45° 4 (15) Find the radius of curvature and the coordinates of the centre of 2 curvature of the curve + 25 16 1 at the point (0, 4). (20) Question 2(a): Determine the smallest positive value of x at which a point of inflexion occurs on the graph of y = 3e3* cos(3x-6). (15) Question 2(b): Question 3(a): (i) Determine whether the following series is convergent or divergent: 2 2 2 2 2x3 3x4 4x5 5x 6 sin x cos x (ii) Evaluate: Lim (10) (10) If the 7th term of an A.P. is 22 and the 12th term is 37, find the first five terms of the series. (10) Question 3(b): By the use of Maclaurin's series, show that tan x=x- + 5 (20)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
Transcribed Image Text:Question 1(a):
The parametric equations of a function are x = 2 cos³0, y = 2sin 30.
Question 1(b):
Find the equations of the tangent and normal at the point for which
元
0=== 45°
4
(15)
Find the radius of curvature and the coordinates of the centre of
2
curvature of the curve
+
25 16
1 at the point (0, 4). (20)
Question 2(a):
Determine the smallest positive value of x at which a point of
inflexion occurs on the graph of y = 3e3* cos(3x-6).
(15)
Question 2(b):
Question 3(a):
(i) Determine whether the following series is convergent or divergent:
2
2
2
2
2x3 3x4
4x5
5x 6
sin x cos x
(ii) Evaluate:
Lim
(10)
(10)
If the 7th term of an A.P. is 22 and the 12th term is 37, find the first five
terms of the series.
(10)
Question 3(b):
By the use of Maclaurin's series, show that tan
x=x-
+
5
(20)
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