Q4 By sketching the graph, find the volume of the solid generated by revolving the region bounded by the parabola, y = x² + 4 and the straight line y = 3x + 14 about the x axis.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter2: Equations And Inequalities
Section2.1: Equations
Problem 76E
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please I want an answer q [ 4]
Q1 Verify that the given complex function is an Analytic Function,
w = f(z) = z³ – 3z – 5
Q2 Find the Maclaurin Series expansion for the function,
1
f(x) =
(1-
4x)2
by writing the first four non-zero terms of the expansion.
Q3 The imaginary part of the complex function f(z) = u + iv is,
v(x, y) = 3x²y + 2x² – y³ – 2y²
(i)
Prove that v(x, y) is harmonic.
(ii)
Find the harmonic conjugate function u(x,y).
Q4 By sketching the graph, find the volume of the solid generated by
revolving the region bounded by the parabola, y = x² + 4 and the
straight line y = 3x + 14 about the x – axis.
Q5 Find the length of the arc of the curve in the given range,
y3
x = 25y + 5y² +
0 <y< 3
4(у + 5)
Q6 By Sketching the graph, find the volume of the solid generated by
revolving the region given by,
y =
9 – (x – 3)² ; 2 <x< 5
about the x - axis.
Q7 Find the image of the circle |Z – 2| < 2 in the z – plane under the
1
inverse transformation w =
; by representing both the regions
graphically.
Transcribed Image Text:Q1 Verify that the given complex function is an Analytic Function, w = f(z) = z³ – 3z – 5 Q2 Find the Maclaurin Series expansion for the function, 1 f(x) = (1- 4x)2 by writing the first four non-zero terms of the expansion. Q3 The imaginary part of the complex function f(z) = u + iv is, v(x, y) = 3x²y + 2x² – y³ – 2y² (i) Prove that v(x, y) is harmonic. (ii) Find the harmonic conjugate function u(x,y). Q4 By sketching the graph, find the volume of the solid generated by revolving the region bounded by the parabola, y = x² + 4 and the straight line y = 3x + 14 about the x – axis. Q5 Find the length of the arc of the curve in the given range, y3 x = 25y + 5y² + 0 <y< 3 4(у + 5) Q6 By Sketching the graph, find the volume of the solid generated by revolving the region given by, y = 9 – (x – 3)² ; 2 <x< 5 about the x - axis. Q7 Find the image of the circle |Z – 2| < 2 in the z – plane under the 1 inverse transformation w = ; by representing both the regions graphically.
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